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 0.02m, what is the frequency of motion?

Answer 1

Answer:

f = 3.97 Hz

Explanation:

Given that,

Centripetal acceleration, $a=13\ m/s^2$

The radius of motion is 0.02 m

The formula for the centripetal acceleration is given by :

$a=\dfrac{v^2}{r}\\\\v=\sqrt{ar} \\\\v=\sqrt{13\times 0.02} \\\\v=0.5\ m/s$

The speed of an object in a circular path is given by :

$v=\dfrac{2\pi r}{t}$

t is time period

Also, f=1/t (f is frequency)

$f=\dfrac{v}{2\pi r}\\\\f=\dfrac{0.5}{2\pi \times 0.02}\\\\f=3.97\ Hz$

Hence, the frequency of motion s 3.97 Hz.