Physics midterm problem: basketball rolling up ramp

Physics 205A Midterm 2, fall semester 2019
Cuesta College, San Luis Obispo, CA

A basketball (mass 0.43 kg, radius 0.11 m) rolls without slipping with a constant initial velocity of 2.4 m/s across a horizontal floor. The basketball begins to roll up a ramp. Determine the highest vertical height that the basketball will reach before rolling back down the ramp. Ignore friction and drag. Show your work and explain your reasoning using the properties of rotational inertia, energy forms, and conservation of energy.

The basketball is a hollow sphere (I_{hollow sphere} = (2/3)·M·R².)


Solution and grading rubric:

• p:
  Correct. Sets up a transfer-balance energy conservation equation with the sum of the changes in translational kinetic energy of the basketball, rotational kinetic energy of the basketball, and gravitational potential energy of the basketball set to zero (as no energy is lost to non-conservative work), fills in all known/given values, and solves for the unknown. (May have ± sign errors for final terms subtracting initial terms, but in a somewhat consistent manner that still results in correct final height of basketball).
• r:
  Nearly correct, but includes minor math errors. Or multiple arithmetic errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Typically omits one of the energy terms, but attempts to apply energy conservation to the remaining two terms.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Calculations of some energy terms, but does not sufficiently tie them together in a transfer-balance energy conservation equation. Typically has only one energy term, or relates an energy term with a non-energy quantity (such as weight, momentum, moment of inertia, etc.).
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach involving methods other than energy conservation.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm02sQm5
p: 26 students
r: 16 students
t: 7 students
v: 3 students
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student 8520):
Another sample "p" response (from student 1203):

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2019
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz05Gu1L



Sections 70854, 70855 results

0- 6 :	** [low = 6]
7-12 :	*********
13-18 :	***********
19-24 :	***************** [mean = 19.8 +/- 6.3]
25-30 :	************* [high = 27]

Online reading assignment: rotational dynamics

Physics 205A, fall semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on rotational dynamics.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"This section is about rolling objects in terms of rolling dynamics, rotational inertia, and angular speed. With these ideas the reading linked them to previous ideas of potential and kinetic energy."

"I somewhat understand how to recognize changes (increases/decreases) in rotational kinetic energy, and how rotational speed ω is related to translational speed v for objects that roll without slipping."

"The concept of balancing the angular speed equation v =r·ω. Larger objects have larger radii and therefore must have a smaller ω to match the velocity of a smaller object."

"As a circular object rolls down a hill without slipping, its gravitational potential energy decreases at the same rate that its (translational kinetic energy + rotational kinetic energy) INCREASES. I also understand that when a circular object that doesn't slip launches off of a ramp, it will maintain the SAME rotational kinetic energy in the air that it had at the moment it left the ramp."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Moment of inertia to be confusing."

"Rotational inertia and inertia in general. I'm also confused on how we relate inertia and energy in the equations given."

"How to find the variables in the equations, they all look like random letters and I don't know what they stand for."

"I think I just need some review to further understand the difference between equations and how to memorize what equation to actually use in a given situation. Otherwise, I feel confident on this subject."

"The concept of rolling motion is still confusing. I'm unsure of what tangential speed really is."

"I'm trying to wrap my head around the rolling motion."

"I would like a little more explanation on all the terms in the energy transfer-balance equation."

"Upon completing the presentation preview, I was very confused about the rotational kinetic energy at first but soon figured it out once given another glance. The rotational kinetic energy depends on rotational inertia and the angular speed of the object."

What is the SI (Système International) unit for rotational kinetic energy?

"J for joules."

"Like other forms of energy, the SI unit for rotational kinetic energy is the joule (J)."

"kg·m²/s²."

Describe an object that only has rotational kinetic energy, and no translational kinetic energy.

"A ceiling fan is an object that has only rotational kinetic energy and no translational kinetic energy."

"A windmill/wind turbine."

"The gear in a watch or machine that only spins and stays stationary."

"A hamster wheel has rotational kinetic energy but no translational kinetic energy."

"It would be an object that continues to spin, but remains in one place, like a Ferris wheel."

"An ice skater spinning in one place would only have rotational kinetic energy but not translational. This is because they are only rotating about an axis, but are not moving through space from one point to another."

"An object can rotate really really fast but its rotational kinetic energy can still be zero as long as it does not have any contact with a solid surface. Example: a car at an auto shop is resting on a lift like in the movie Feris Bueller's Day Off, and the rear wheels are rotating really fast, but since there no contact with the ground the car is not moving anywhere and transitional kinetic energy is zero."

"Any wheel that spins around a fixed axis."

"I'm not 100% on understanding this but I think a compact disc would have rotational kinetic energy but not translational because it isn't moving."

"I'm not sure on this one."

Describe an object that has both translational kinetic energy and rotational kinetic energy.

"A ball rolling down a hill."

"The wheels on a skateboard which are both rotating and moving forward."

"A unicycle."

"A car driving on the walls of a circle."

"The teacup ride at Disneyland is an example of an object with both rotational and translational kinetic energies because it is rotating about an axis as well as moving from one point in space to another."

"I need further instruction on this."

"I am not sure."

From starting at the top of the ramp to the bottom of the ramp, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: decreases [76%]
Translational kinetic energy: increases [78%]
Rotational kinetic energy: increases [80%]

From starting at the top of the ramp to the bottom of the ramp, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	****************** [18]
translational kinetic energy.	***** [5]
rotational kinetic energy.	********* [9]
(There is a tie.)	******* [7]
(Unsure/lost/guessing/help!)	******* [7]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: increases [76%]
Translational kinetic energy: decreases [57%]
Rotational kinetic energy: no change [43%]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	****************** [18]
translational kinetic energy.	********* [9]
rotational kinetic energy.	*** [3]
(There is a tie.)	******** [8]
(Unsure/lost/guessing/help!)	******** [8]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Can we go over specific examples for each type of energy showing when each energy increases and decrease?"

"I am EXTREMELY confused how to tell the difference between the gravitational, rotational, and translational energies. May we have a quick simple break down summary in class?"

"I'm liking the colder weather."

"Q: How does a German physicist drink beer? A: With ein Stein."

Physics midterm question: rotational kinetic energies of basketball vs. tennis ball

Physics 205A Midterm 2, fall semester 2018
Cuesta College, San Luis Obispo, CA

A basketball (mass 0.43 kg, radius 0.11 m) and a tennis ball (mass 0.058 kg, radius 0.033 m) 
both roll without slipping across a horizontal floor with the same constant speed of 0.50 m/s. Discuss why the basketball will have more rotational kinetic energy than the tennis ball.



Both objects are hollow spheres (I = (2/3)·M·R²).

Solution and grading rubric:

• p:
  Correct. Numerically calculates for each ball the angular speed from the v = R⋅ω condition for rolling without slipping, and moment of inertia I = (2/3)·M·R², and then includes both these factors to compare the rotational kinetic energy KE_rot = (1/2)⋅M⋅ω^2 of both objects, such that the basketball has a larger numerical value for the rotational kinetic energy than the tennis ball.
• r:
  As (p), but argument indirectly, weakly, or only by definition supports the statement to be proven, or has minor inconsistencies or loopholes.
• t:
  Nearly correct, but argument has conceptual errors, or is incomplete. At least shows that the basketball has a higher moment of inertia than the tennis ball, but claims that they have the same angular speed, or does not explicitly show that difference in angular speeds is much smaller than the difference in moments of inertia in determining that the basketball has a greater rotational kinetic energy.
• v:
  Limited relevant discussion of supporting evidence of at least some merit, but in an inconsistent or unclear manner.
• x:
  Implementation/application of ideas, but credit given for effort rather than merit.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855
Exam code: midterm02r3iN
p: 17 students
r: 2 students
t: 37 students
v: 1 student
x: 0 students
y: 0 students
z: 0 students

A sample "p" response (from student):

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2018
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz05Ro74



Sections 70854, 70855 results

0- 6 :
7-12 :	******** [low = 9]
13-18 :	**************
19-24 :	************************* [mean = 19.6 +/- 5.2]
25-30 :	***** [high = 30]

Online reading assignment: rotational dynamics

Physics 205A, fall semester 2018
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on rotational dynamics.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"The differences between rotational and translational kinetic energies."

"Rotational inertia depends on the mass and size of an object."

"That rotational parameters and translational parameters are related to each other by the radius of the object that rolls without slipping. I also understood that the higher the rotational speed, the higher the rotational kinetic energy."

"I understand the basic concept of angular speed and how it relates to translational speed. I get that the angular speed can be the same between two rolling objects, but if the radii are different, the objects will travel at different speeds."

"Rotational inertia is a property of an object which can be rotated. There is a relationship between the mass and the rotational inertia of an object. Rotational kinetic energy is the energy of rotational motion."

"Angular velocity describes the motion of a rigid object rotating about a fixed axis. A change in velocity means angular acceleration is occurring. The net external torque is proportional to angular acceleration."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Rolling without slipping. Rotational kinetic energy term in the transfer/balance equation."

"Angular speed and rotational inertia--I would like to see examples of these problems worked out."

"There were so many equations how do I apply them?"

"Although I read it over and over again, I found it hard understanding what rotational inertia means."

"I found the majority of this section to be very confusing. I still don't really understand how to calculate anything, how angular speed and rotational kinetic energy relate, and pretty much anything related to rotational inertia."

"Applying the transfer/balance equation to situations is kinda difficult to grasp. How can you figure out which energy system experienced a greater change?"

"I think I'm getting what's going on!"

"I understood pretty much everything in this chapter."

What is the SI (Système International) unit for rotational kinetic energy?

"J (joules)."

"Joules (kg·m²/s²)."

"(1/2)·I·ω²."

"I have no idea :( "

"I just didn't get to this (yet)."

Describe an object that only has rotational kinetic energy, and no translational kinetic energy.

"A hamster wheel that spins in place."

"A top that spins."

"A stationary table saw that spins in order to cut wood."

"A wheel of a car getting brake-tested or balanced on a stationary platform."

"Windmill."

"Ice skater spinning."

"A Ferris wheel."

"A ball connected to a string being spun in a circle."

Describe an object that has both translational kinetic energy and rotational kinetic energy.

"A wheel rolling down a hill."

"Tire rolling across the ground."

"A hamster ball."

"A Solowheel has both translational kinetic energy and rotational kinetic energy."

"A hula hoop rolling across the floor without slipping."

"Skateboards."

From starting at the top of the ramp to the bottom of the ramp, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: decreases [81%]
Translational kinetic energy: increases [85%]
Rotational kinetic energy: increases [77%]

From starting at the top of the ramp to the bottom of the ramp, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	*********** [11]
translational kinetic energy.	********* [9]
rotational kinetic energy.	******* [7]
(There is a tie.)	*********** [11]
(Unsure/lost/guessing/help!)	********* [9]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: increases [87%]
Translational kinetic energy: decreases [61%]
Rotational kinetic energy: no change [40%]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	********************* [21]
translational kinetic energy.	******* [7]
rotational kinetic energy.	***** [5]
(There is a tie.)	***** [5]
(Unsure/lost/guessing/help!)	********* [9]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"I have a question not necessarily on this reading assignment, but rather from the collisions section. Going over the practice quiz one of the options when comparing various different collisions there was an option to pick: 'translational kinetic energy and/or momentum cannot be determined.' I was wondering if there is ever a situation during a collision that conservation for either quantity can't truly be determined?" (Only if the presence (or absence) of external forces during the (brief) collision are unknown. If there are external forces present during the collision, then both quantities can't be conserved. If there are no external forces during the collision, then momentum is conserved, but translational kinetic energy may or may not be conserved depending on the rebound/damage incurred by the colliding objects.)

"For the tire rolling down the ramp, I concluded that gravitational potential energy must have experienced the greatest change since its decrease contributed to the increases in both translational kinetic energy and rotational kinetic energy?" (Yes.)

"Can you explain what happens to the rotational kinetic energy of the tire after it leaves the ramp?" (Since we ignore drag, the rotation of the tire is unaffected as it sails through the air, so its rotational kinetic energy remains constant.)

"I am doing my best to pass the quiz tomorrow. I am battling the pace of the class and also the 'flipped' structure (no need to reiterate my or your perspective on this). I really am trying to not hate physics."

"Enjoying the class so far."

"Would you rather be able to see 10 minutes into your own future or 10 minutes into the future of anyone but yourself?" (I'm not sure if it was better to have seen myself reading this question 10 minutes into the future, or to have seen you sending me this question 10 minutes into the future.)

Physics quiz question: ring vs. smaller disk of same mass

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

A ring and a solid disk rotate about their centers. The ring and the solid disk each have the same mass of 1.2 kg. The ring has a radius of 0.25 m, and the solid disk has a smaller radius than the ring. (I_ring = M·R², I_disk = (1/2)·M·R².)

The rotational inertia of the ring is __________ the rotational inertia of the solid disk.
(A) less than.
(B) equal to.
(C) greater than.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

The rotational inertia of the ring of mass M = 1.2 kg and radius R = 0.25 m is:

I_ring = M·R² = (1.2 kg)·(0.25 m)² = 0.075 kg·m².

The rotational inertia of the disk of mass M = 1.2 kg and a radius smaller than 0.25 m, along with the factor of (1/2) then must be smaller than the rotational inertia of the ring:

I_disk = (1/2)·M·R² = (1/2)·(1.2 kg)·(some value less than 0.25 m)²,

such that I_ring > I_disk.

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 6 students
(B) : 4 students
(C) : 39 students
(D) : 0 students

Success level: 80%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.34

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, version 1
Exam code: quiz05nWaW



Sections 70854, 70855 results

0- 6 :
7-12 :	***** [low = 9]
13-18 :	***************
19-24 :	********************* [mean = 19.7 +/- 4.8]
25-30 :	***** [high = 27]

Online reading assignment: rotational dynamics

Physics 205A, fall semester 2017
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on rotational dynamics.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Angular speed = angular displacement/time. The distance a car moves is equal to the arc length the tire rolls."

"How to calculate the KE_rot and all that. Its a little unclear but I think I understand that the most."

"When an object has both rotational kinetic energy and translational kinetic energy."

"Rotational kinetic energy is the energy of rotational motion. The faster an object rotates, the more KErot energy it has. Objects can have both rotational kinetic energy and translational kinetic energy."

"There is a lot of information. I understand the difference between translational and rotational speed, and the relationship between mass, and rotational inertia, and that all of these factors allow for different equations that calculate inertias for different objects. The transfer/balance equations are straightforward."

"I will be honest, I spent today studying for the quiz on Monday and am scared learning new material right now will interfere with the material I am trying to make sure I know for tomorrow. I did attempt the homework though."

"Honestly I didn't understand anything from the reading."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Most of this is very confusing. A lot of new stuff at once is hard, especially when trying to study for a quiz that doesn't involve this new material."

"Most of this, actually."

"The difference between rotational kinetic energy and translational kinetic energy."

"I understand that rotational kinetic energy and translational kinetic energy are different. However, apart from that, I think I might need a better understanding on the differences between the two."

"I need more explanation on angular speed. And the gravitational potential energy, the translational kinetic energy, and the rotational kinetic energy."

"Rolling without slipping--I would appreciate going over this in class."

"KE_tr and KE_rot is little confusing and it would be nice to go over it in class."

"Moments of inertia. I do not know where to begin for applications."

"I understand this section."

What is the SI (Système International) unit for rotational kinetic energy?

"kg·m²/s²."

"J, joules."

"rad/s?"

Describe an object that only has rotational kinetic energy, and no translational kinetic energy.

"Anemometer."

"Spin bike."

"Carousel ride."

"A record spinning."

"A spinning basketball on someone's finger."

"Windmill."

"House fan."

"Hamster wheel; Ferris wheel."

"Doorknob."

Describe an object that has both translational kinetic energy and rotational kinetic energy.

"Bicycle rolling down a hill."

A unicycle."

"A tire rolling down and in contact with a road."

From starting at the top of the ramp to the bottom of the ramp, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: decreases [84%]
Translational kinetic energy: increases [86%]
Rotational kinetic energy: increases [79%]

From starting at the top of the ramp to the bottom of the ramp, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	************** [14]
translational kinetic energy.	**** [4]
rotational kinetic energy.	***** [5]
(There is a tie.)	********** [10]
(Unsure/lost/guessing/help!)	**** [4]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: increases [78%]
Translational kinetic energy: decreases [68%]
Rotational kinetic energy: no change [43%]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	************** [14]
translational kinetic energy.	****** [6]
rotational kinetic energy.	**** [4]
(There is a tie.)	****** [6]
(Unsure/lost/guessing/help!)	******* [7]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"I found the tire rolling down the mega-ramp oddly satisfying."

"Go over how to find values for KE_tr and KE_rot)."

"Could you use these equations to predict how a certain tire made at different masses would be ideally and most efficient at rolling?" (Yes, we can.)

"If energy can be converted from one form to the other does that mean all energy types should have the same SI unit?" (Yes!)

"I'm going to need a lot of review on this, I'm pretty confused..."

"Need lots of help with this in class!"

"I am desperate! I can't catch up the pace--I understand the content but it takes me forever to do all the exercises, read the book, blog and try to understand the lab beforehand...and I never procrastinate! :( Sad!"

"I need to work on my time management."

Physics quiz question: hammer throw chain length

Physics 205A Quiz 5, fall semester 2016
Cuesta College, San Luis Obispo, CA

"2010 Asian Games - Men's Hammer Throw Final"
cctv7military
youth.be/DGsuBw0A-r8

The "hammer" used in a hammer throw competition can be approximated[*] as a ball spun in a circle at the end of a chain of negligible mass, with a rotational speed of 24 rad/s. The rotational inertia of the ball and chain system is 11 kg·m². (I_{point mass} = m·r².) If the mass of the ball is 7.3 kg, the length of the chain is:
(A) 0.66 m.
(B) 1.2 m.
(C) 1.5 m.
(D) 2.2 m.

[*] wired.com/2012/08/olympics-physics-hammer-throw/

Correct answer (highlight to unhide): (B)

The rotational inertia of a point mass m and moving in a circle of radius r is:

I_{point mass} = m·r²,

such that solving for the radius (which would be the length of the chain):

r² = I_{point mass}/m,

r = √(I_{point mass}/m),

r = √((11 kg·m²)/(7.3 kg)) = 1.227537907792867 m,

or to two significant figures, the chain length is 1.2 m.

(Response (A) is m/I_{point mass}; response (C) is √(m·g/I_{point mass}); response (D) is m·g/I_{point mass}.)

Sections 70854, 70855, 73320
Exam code: quiz05b0oM
(A) : 4 students
(B) : 32 students
(C) : 14 students
(D) : 5 students

Success level: 58%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.38

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2016
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz05b0oM



Sections 70854, 70855, 73320 results

0- 6 :	*** [low = 6]
7-12 :	***********
13-18 :	************************* [mean = 16.6 +/- 6.0]
19-24 :	************
25-30 :	* [high = 30]

Physics final exam problem: rolling spool non-conservative energy losses

Physics 205A Final Exam, fall semester 2015
Cuesta College, San Luis Obispo, CA

"Hilarious moving company accident!"
ME5723
youtu.be/jo3ohNxEGkM

A spool of cable (approximated as a disk of 0.90 m radius and 80 kg mass) is rolled up a ramp built on a flight of stairs. It is (accidentally) released from rest, rolls down the ramp, and has a final speed of 12 m/s as it reaches the bottom of the ramp[*]. If the spool was released from a vertical height of 14 m above the bottom of the ramp, determine how much energy (if any) was lost to drag/friction. Show your work and explain your reasoning using the properties of rotational inertia, energy forms, and (non-)conservation of energy.

(Given: I_disk = (1/2)·M·R².)

[*] youtu.be/jo3ohNxEGkM.

Solution and grading rubric:

• p:
  Correct. Sets up a transfer-balance energy conservation equation with changes in translational kinetic energy, rotational kinetic energy (with the rolling without slipping condition), and gravitational potential energy, and finds the amount of energy lost to drag/friction, which is the sum of all these changes in total mechanical energy forms.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. At least enough steps are shown that would theoretically result in a complete answer, multiple errors notwithstanding.
• v:
  Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Calculations of some energy terms, but does not sufficiently tie them together in a transfer-balance energy conservation equation.
• x:
  Implementation of ideas, but credit given for effort rather than merit. Approach involving methods other than energy conservation.
• y:
  Irrelevant discussion/effectively blank.
• z:
  Blank.

Grading distribution:
Sections 70854, 70855, 73320
Exam code: final7rUk
p: 13 students
r: 14 students
t: 23 students
v: 11 students
x: 5 students
y: 2 students
z: 2 students

A sample "p" response (from student 1114):

Online reading assignment: rotational dynamics

Physics 205A, fall semester 2016
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on rotational dynamics.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Angular velocity is radians per second. Rotational kinetic energy is fixed about an axis and must have a moment of inertia."

"I appreciate how translational and kinetic energies are related. I have a fascination with kinetic energy and how it corresponds with other bodies."

"A rolling object's translational speed is determined by multiplying the radius of the object by the angular speed of the object. v = r·ω."

"That if two rolling objects have the same velocity, the one with a smaller radius will have a bigger angular speed, and the one with the larger radius will have a slower angular speed."

"How a rolling object with a smaller radius has a faster ω angular speed in order to keep up with an object with a larger r radius which will have a slower angular speed as it roles."

"That translation and rotational kinetic energy is related via velocity, and that rotational kinetic energy can also be figured into energy conservation equations."

"The inputs to the equations and what each equation represents, however I just need to see some examples and work done to fully grasp the material."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I have never been great with calculating rotational kinetic energies. There's somethingoing about energy and inertia that I have difficulty with discerning when talking about something like a wheel."

"I don't understand what rotational energy is."

"I'm a little confused on the concept of inertia. What is inertia? How does it relate to angular speed?"

"I am having trouble understanding at which exact moment energy changes in a system."

"The difference between rotational energy and translational energy, how can they be independent of one another?"

"I am slightly confused on how an object can have both translational and rotational kinetic energy. The total energy conservation equation is a little confusing as well. I think seeing a problem worked out in class will be very helpful."

What is the SI (Système International) unit for rotational kinetic energy?

"J, joules."

"Radians?"

"Radians per second?"

"kg·m²?"

Describe an object that only has rotational kinetic energy, and no translational kinetic energy.

"A spinning top."

"A beach ball rotating in place in a pool of water."

"A Ferris wheel"

"A windmill because it is not moving, just rotating."

"A hamster wheel that is stuck in place but cannot roll forwards or backwards or any other direction."

"Blades in a blender don't have translational energy because the blades only rotate and they aren't moving other than spinning around the axis."

"A clothes dryer."

"A wind turbine."

"Anything that will stay in place but rotate on an axis."

Describe an object that has both translational kinetic energy and rotational kinetic energy.

"Rolling a ball down an incline."

"A bicycle going down a hill."

"Earth"

"A rider on a Solowheel."

"A car is driving down a road, while the tire goes around it has a translational kinetic energy for how fast it is going, but it also has a rotational kinetic energy to show how fast the circular rotation is going."

"A launched ball spinning in the air."

"An object moving in a single direction as well as rotating around an axis."

"I am unsure about this concept and how it would have both?"

From starting at the top of the ramp to the bottom of the ramp, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: decreases [83%]
Translational kinetic energy: increases [74%]
Rotational kinetic energy: increases [78%]

From starting at the top of the ramp to the bottom of the ramp, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	***************** [17]
translational kinetic energy.	****** [6]
rotational kinetic energy.	********* [9]
(There is a tie.)	****** [6]
(Unsure/lost/guessing/help!)	******** [8]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: increases [74%]
Translational kinetic energy: decreases [50%]
Rotational kinetic energy: no change [39%]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	*************** [15]
translational kinetic energy.	********* [9]
rotational kinetic energy.	*** [3]
(There is a tie.)	********** [10]
(Unsure/lost/guessing/help!)	********* [9]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"I think the gravitational potential energy should increase/decrease the most in both tire situations because KE_trans and KE_rot are both changing in the same 'direction' (increase/decrease) so gravitational PE_grav needs to change as much as those two added together meaning it should be the biggest. Is that wrong thinking?" (Yes, if the tire both rolled downhill, or back up a hill. But since the tire as it moves upwards is in mid-air, not rolling up a hill, the KE_rot doesn't change (its rotational speed stays constant.)

"Does a tire having 'rolling with slipping' need to be on a frictionless surface or a wet surface?" (Yes, or if the tire is "burning rubber" at the very start of a drag race.)

"Will we be practicing the tire problems in class?"

"Not sure how to apply the conservation of energy equations here."

"I would like some conceptual basics gone over in class and not just example problems."

"Examples would be helpful for relationship between rotational and translational kinetic energy."

"How can we tell which type of energy has the biggest change?"

"I need help on rotational kinetic energy."

"Will we learn about the physics of waves? Not sound waves but waves in the ocean or lake." (Primarily one-dimensional waves along strings/wires/ropes/cables, but those concepts can be extended to any kind of waves that travel through water or air.)

Physics quiz question: moment of inertia of LP record

Physics 205A Quiz 5, fall semester 2015
Cuesta College, San Luis Obispo, CA

"I have a vinyl fetich"
Christmas Junkie
flic.kr/p/fFwATx

An LP record[*] has a rotational inertia of 1.46×10^–3 kg·m², and rotates at a rate of 3.5 rad/s. The record can be considered a solid disk (I_disk = (1/2)·M·R²). If the LP record then rotates at a slower rate, it would have __________ rotational inertia.
(A) more.
(B) the same.
(C) less.
(D) (Not enough information is given.)

[*] Peter Atkins, Julio de Paula, Physical Chemistry (9th ed.), W.H. Freeman and Co. (2009), p. 318.

Correct answer (highlight to unhide): (B)

Since rotational inertia of the LP record depends on its mass M and radius R, which do not physically change whether rotating at a faster or slower rate, then the rotational inertia remains constant.

Sections 70854, 70855, 73320
Exam code: quiz05bL8D
(A) : 24 students
(B) : 32 students
(C) : 9 students
(D) : 0 students

Success level: 48%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.74

Physics quiz archive: rotations, torque, pressure, buoyancy, fluid flow

Physics 205A Quiz 5, fall semester 2015
Cuesta College, San Luis Obispo, CA
Sections 70854, 70855, 73320, version 1
Exam code: quiz05bL8D



Sections 70854, 70855, 73320 results

0- 6 :	** [low = 0]
7-12 :	****************
13-18 :	************************** [mean = 17.2 +/- 6.1]
19-24 :	**************
25-30 :	******** [high = 30]

Online reading assignment: rotational dynamics

Physics 205A, fall semester 2015
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing a presentation on rotational dynamics.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Rotational inertia depends on mass and radius, while the rotational kinetic energy depends on rotational inertia and angular speed (squared)."

"An object with both translational motion and rotational motion also has translational kinetic energy and rotational kinetic energy."

"It is cool to think about how similar the translational speed and the angular speed of a rolling object are related, and the relationship between mass and the rotational inertia of the object."

"An object doesn't have to possess both translational and rotational kinetic energies at the same time. Rotational kinetic energy is the energy of a rotational motion about an axis, and it depends on the rotational inertia of the object. Translational kinetic energy depends on motion through space. There are formulas to calculate these kinetic energies, but that part I am currently struggling with.

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I understand the concept of rotational inertial, moment of inertia, and rotational kinetic energy. However, when it comes down to applying it to the given problems it gets somewhat confusing."

"I found some of the symbols to be confusing. I will get used to the symbols though."

"The difference between rotational kinetic energy and translational kinetic energy really confuses me."

"Nothing quite yet. Usually my questions come with clarifications while in class, when we get more of an exposed understanding."

"I find the formulas/equations for this assignment extremely confusing to follow along with. Hopefully with some in class examples and practice I will be able to use them correctly."

What is the SI (Système International) unit for rotational kinetic energy?

"Joules."

"kg·m²/s²."

"rev/s or rad/s."

"rad/s²."

Describe an object that only has rotational kinetic energy, and no translational kinetic energy.

"Hamster wheel."

"Windmill."

"Stationary bike."

"A record turntable."

"Any object on a fixed axis."

"I am not sure."

Describe an object that has both translational kinetic energy and rotational kinetic energy.

"A ball rolling down the street."

"A tire rolling down a hill."

"Driving a car--it has both transnational kinetic energy and rotational kinetic energy, because the wheels must rotate to move the car and which also must translate."

"I'm not sure how to describe an example."

From starting at the top of the ramp to the bottom of the ramp, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: decreases [69%]
Translational kinetic energy: increases [75%]
Rotational kinetic energy: increases [78%]

From starting at the top of the ramp to the bottom of the ramp, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	************* [13]
translational kinetic energy.	***** [5]
rotational kinetic energy.	************ [12]
(There is a tie.)	******************* [19]
(Unsure/lost/guessing/help!)	********** [10]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, indicate the changes in each of the energy forms of the tire.
(Only correct responses shown.)

Gravitational potential energy: increases [63%]
Translational kinetic energy: decreases [48%]
Rotational kinetic energy: no change [39%]

For the subsequent part of this stunt, from just as it leaves the second ramp to reaching the top of its trajectory, the energy form that experienced the greatest amount of change (increase or decrease) was the tire's:

gravitational potential energy.	******************** [20]
translational kinetic energy.	******* [7]
rotational kinetic energy.	******* [7]
(There is a tie.)	************ [12]
(Unsure/lost/guessing/help!)	************* [13]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"I would like to know how the rotational inertia factors are what they are. How are they derived?" (Integral calculus. You don't want to go there.)

"Will we have to memorize all of these equations or will they be given to us?" (You will be given all the equations you need for the quizzes and exams. And rotational inertia for any relevant object.)

"The textbook sections were so hard to read. The blog simplified it but being taught what equations to use and how to decipher problems would be helpful."

"I enjoyed reading about this section."

"Why is m·r² called the 'moment of inertia?'" (Because, integral calculus. Actually m·r² is the rotational inertia of a single point mass, if you have a distribution of point masses that make up an extended object, then to find the rotational inertia of that object you would need to add up all of its individual point-mass rotational inertiae--that is, integrate m·r² over the entire object. #notgoingthere)

"What is your ideal temperature? Mine is 66°F." (Cool. Cool cool cool.)

"I secretly want to become a mechanic, because I'm in love with cars but I'm also working towards becoming a physician's assistant. So why not do both? #hatersgonnahatesomemore" (#learnallthethings)