An object moving in a circular motion has a centripetal acceleration of 100 𝑚𝑠−2. If theradius of the motion is 0.25 m, calculate the frequency of the motion

To calculate the frequency of the motion, we first need to find the speed of the object. We can use the formula for centripetal acceleration, which is a = v^2 / r, where a is the acceleration, v is the speed, and r is the radius.

Rearranging the formula to solve for v gives us v = sqrt(a * r). Substituting the given values gives us v = sqrt(100 m/s^2 * 0.25 m) = 5 m/s.

The frequency of the motion is the number of times the object completes a full circle per second. The distance around the circle (the circumference) is 2 * pi * r = 2 * pi * 0.25 m = 0.5 pi m.

The speed of the object is the distance it travels per second, so the frequency is v / (2 * pi * r) = 5 m/s / 0.5 pi m = 10 / pi Hz.

So, the frequency of the motion is approximately 3.18 Hz.