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...