# 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.

3 Circular Motion Problems

1. A circular disk of radius 30 cm is rotating with an angular acceleration of 1 radian/ s2. What is the tangential acceleration of a point on the rim of the disk? What is its centripetal acceleration if the angular speed is 3 rev / s?

2. A 980 Kg car traveling at 20 m/s rounds a curve of radius 40 m. What is the friction force that must act on the car to keep it in its circular path?

3. An object with a mass of 100 Kg is dragged up an incline by applying a force F. The total distance moved along the incline is 200 m and the vertical height gained in moving this distance is 20 m. What is the magnitude of the force F if friction is negligible? (Assume g = 10 m/s2)

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