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
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.