Rotational Dynamics with Friction

Dissipative effects and models with friction. Covers: Worked Examples in Rotational Motion with Friction.

General idea of the topic

Friction on a body that spins or rolls plays two roles: it can brake the motion, and it can be the force that makes it possible. In a wheel rolling without slipping, static friction does not dissipate energy; it produces the moment that accelerates the spin and reduces the acceleration of the center.

The topic gathers worked examples that combine the second law of translation for the center of mass, the one for rotation about it and the constraint between the two, with and without slipping.

What you will truly understand

By the end you will be able to decide whether a body rolls without slipping or slides, compute the required friction force and check that it does not exceed the maximum.

You will also know why a cylinder goes down a plane more slowly than a block sliding without friction.

Recommended learning route

1. Worked Examples in Rotational Motion with Friction: worked examples of rotation and rolling with friction, with the complete setup and the check of the regime.

Physical criterion you must acquire

The essential criterion is to assume rolling without slipping, solve and check that the friction force obtained does not exceed μN. If it does, the body slides and the calculation must be repeated with kinetic friction, without the constraint between linear and angular acceleration.

Connection with real problems

• wheels that start or brake.
• billiard and bowling balls.
• cylinders and spheres rolling on planes.
• vehicle traction.

Final goal of the topic

The final goal is to solve rotation and rolling problems with friction methodically and justify the regime of each contact.