## Period of a Planet

Suppose that the gravitational force varies inversely as the $$n^{th}$$ power of the distance. Then, the period of a planet in circular orbit of radius $$R$$ around the sun will be proportional to (A) $$R^{\frac{n+1}{2}}$$ (B)$$R^{\frac{n-1}{2}}$$ (C) $$R^n$$ (D)...

## Button on a Rotating Platform

A small button placed on a horizontal rotating platform with diameter $$0.320m$$ will revolve with the plate when it is brought up to a speed of $$40rev/min$$, provided the button is no more than $$0.150m$$ from the axis. What is the coefficient of static friction...

## Minimum Speed of a Rotating Pail of Water

You tie a cord to a pail of water and you swing the pail in a vertical circle of radius $$0.6m$$. What minimum speed must you give the pail at the highest point of the circle if no water is to spill from it? SET UP: The water moves in a vertical circle. The target...

## The Conical Pendulum Problem

An inventor designs a pendulum clock using a bob with mass m at the end of a thin wire of length L. Instead of swinging back and forth, the bob is to move in a horizontal circle with constant speed v, with the wire making a fixed angle $$\beta$$ with the vertical...