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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...tact point on the ground remains instantaneously stationary, while the centre of mass moves above it. This causes the disk to rotate about the point of contact with the ground.

It should be obvious then that the maximum force that can be applied before the disk slides rather than rolls is one that is equal to the maximum force of static friction:

Fstatic = u*mg

This is because the torque that causes the disk to rotate depends on the force of static friction at the contact point - that contact point must remain stationary. The force of static friction will exactly oppose the applied force P right up until the point of slip.

T = F x R

Since the force acts parallel to the surface, it is perpendicular to the radius of ...