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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?

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.

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