# Mechanics Angular Acceleration Quantities

A uniform rigid disk of radius r and mass m rolls without slipping on a smooth horizontal surface. A constant force of magnitude P is applied to the rim of the disk at distance r above the horizontal surface and in the direction of motion. r,m,P are known.

what is the angular acceleration in terms of known quantities, and what force P will cause the disk to begin slipping if the coefficient of static friction is u between disk and horizontal surface? what distance d will the disk's center of mass have traveled when it reaches a speed v?

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#### Solution Preview

A uniform rigid disk of radius r and mass m rolls without slipping on a smooth horizontal surface. A constant force of magnitude P is applied to the rim of the disk at distance r above the horizontal surface and in the direction of motion. r,m,P are known.

What is the angular acceleration in terms of known quantities, and what force P will cause the disk to begin slipping if the coefficient of static friction is u between disk and horizontal surface? what distance d will the disk's center of mass have traveled when it reaches a speed v?

Answer:

First, a quick sketch to give us an idea of what is happening:

The torque on the disk is a little strange, but we'll get to that. The rolling motion occurs because the ...

#### Solution Summary

The mechanics of angular acceleration quantities are given. The static friction between disk and horizontal surfaces are analyzed.