A CD has a diameter of 12.0 cm. If the CD is rotating at a constant angular speed of 20.0 radians per second, then the frequency of the rotational motion is
A) 2.14 Hz.
B) 3.18 Hz.
C) 3.83 Hz
D) 4.50 Hz.
E) 4.89 Hz.

Question

Quizplus · Accepted Answer

The formula for the frequency of rotational motion is f = w/2π, where f is the frequency in Hz and w is the angular speed in radians per second.

Given that the CD has a diameter of 12.0 cm, the radius (r) is half of that, or 6.0 cm.

The linear speed (v) of a point on the edge of the CD can be found using the formula v = r × w, where w is the angular speed in radians per second. 
So, 
v = 6.0 cm × 20.0 rad/s = 120 cm/s

The period (T) of one rotation can be found using the formula T = 2πr/v. 
So, 
T = 2π × 6.0 cm / 120 cm/s = 0.314 s

The frequency (f) is the inverse of the period, so 
f = 1/T = 1/0.314 s = 3.18 Hz

Therefore, the best choice is B.

A CD Has a Diameter of 12