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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

Question

An object moving in a circular motion has a centripetal acceleration of 100 𝑚𝑠−2.

If the radius of the motion is 0.25 m, calculate the frequency of the motion.

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Solution

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.

This problem has been solved

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