Physics quiz question: circular saw blade

Physics 8A Quiz 5, Spring Semester 2007
Cuesta College, San Luis Obispo, CA

Physics 8A learning goal Q5.2

[3.0 points.] Consider a circular saw blade 0.120 m in radius that requires 10.0 s to rotate counterclockwise through 200 radians. The initial angular velocity w_0, at the beginning of this time interval, is +21.0 rad/s. (The blade is always rotating counterclockwise.)

Which one of the following statements best describes the magnitude of the final angular velocity w of the blade at the end of the 10.0 s interval, compared to the magnitude of the initial angular velocity w_0?
(A) w < w_0.
(B) w = w_0.
(C) w > w_0.
(D) (Not enough information is given to determine how the magnitude of the final angular velocity compares to the magnitude of the initial angular velocity.)

(Cf. Young and Freeman, University Physics, 11/e, Exercise 9.15.)

Correct answer: (A)
Assuming that the saw blade turns at a constant rate, it will rotate through (21.0 rad/s)*(10.0 s) = 210 radians. Since it actually rotates through 200 radians during this time, it must be slowing down, and thus its final angular velocity w is slower than its initial angular velocity w_0.

Student responses:
(A) : 23 students
(B) : 2 students
(C) : 9 students
(D) : 2 students