# Centripetal acceleration and velocity

A. What is the relationship between the radius and the velocity of a rotating object?

B. What is the relationship between the velocity of a rotating object and the centripetal force exerted on it?

C. The Moon orbits Earth at a distance of about 3.84 × 10^8 m in a path that takes 27.3 days to

complete. What is the centripetal acceleration of the Moon?

D. What is the relationship between the mass of a rotating object and its velocity?

E. When graphing the values of velocity versus velocity squared, did you notice any differences? Explain your answer.

F. When a bucket of water is swung in a vertical circle, the water will remain in the bucket if the velocity is kept high enough. If you let the bucket slow down too much, the water will spill out. The critical velocity is the slowest velocity necessary to keep the water in the bucket.

What is the critical velocity if the formula is: velocity= Sqrt (rg) , where the radius of your arm swing including the bucket is r and g is the acceleration of gravity?

Hint: You must measure or estimate the length from your shoulder to the center of the bucket to determine the radius.

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#### Solution Summary

The solution consists of discussions pertaining to the given questions.

One along a straight line and the other along a curved path.

One of the toughest problem in Dynamics.

Problem-

At the instant shown, car A has a speed of 20 km/h, which is being increased at the rate of 300 km/h2 as the car enters an expressway. At the same instant, car B is decelerating at 250 km/h2 while traveling forward at 100 km/h. Determine the velocity and acceleration of A with respect to B.