Question

An object that moves in uniform circular motion has a centripetal acceleration of 13 m/s^2. If the radius of the motion is o.o2 m, what is the frequency of the motion

Answer 1

To find the frequency of the motion, we can use the following formula:

a_c = ω^2r

Where:
a_c = centripetal acceleration (13 m/s^2)
r = radius of motion (0.02 m)
ω = angular velocity
f = frequency

First, calculate the angular velocity (ω):

a_c = ω^2r
13 = ω^2 * 0.02
ω^2 = 13 / 0.02
ω^2 = 650
ω = √650
ω ≈ 25.49 rad/s

Next, calculate the frequency (f):

f = ω / 2π
f = 25.49 / (2π)
f ≈ 4.05 Hz

Therefore, the frequency of the motion is approximately 4.05 Hz.