help...rotational motion?

Question

As a logging truck rounds a bend in the road, some logs come loose and begin to roll without slipping down the mountainside. The mountain slopes upward at 48.0 degrees above the horizontal, and we can model the logs as solid uniform cylinders of mass 525 kg and diameter 1.20 m.

Find the acceleration of the logs as they roll down the mountain.

What is the friction force on the rolling logs?

Answer 1

You know the equations for sliding with no friction. The grav. force accelerates the translational motion of the sliding block. Here the force produces additional motion, rotational acceleration of the log's moment of inertia. The moment of inertia can be represented as an additional mass that must be accelerated. In the case of a rolling solid cylinder, this mass is m/2. Thus log acceleration a = gmsin(theta)/(1.5m) = 2/3 * gsin(theta). The friction force Ff is what accelerates the rotation of the log. Ff = 0.5*ma or 1/3 * mgsin(theta).