A CD 25 cm is diameter rotates 35 times per minute. Find its centripetal acceleration. (show your solution)
Given:
Diameter of CD, D = 25 cm
Radius of CD, r = D/2 = 12.5 cm = 0.125 m
Angular velocity, ω = 35 rotations/minute = 35 x 2π radians/60 seconds = 3.67 rad/s
The centripetal acceleration, ac, can be calculated using the formula:
ac = r x ω^2
Substitute the values:
ac = 0.125 m x (3.67 rad/s)^2
ac = 0.125 m x 13.47 m^2/s^2
ac = 1.68 m/s^2
Therefore, the centripetal acceleration of the CD rotating at 35 times per minute is 1.68 m/s^2.