Rolling Without Slipping

When a rigid body rolls down an incline without slipping, its translational motion and rotational motion are strongly coupled. The static friction acting at the contact point provides the torque necessary to spin the object, causing its mechanical energy to be split between translation and rotation. Because static friction acts at an instantaneously stationary contact point, it does no macroscopic work, and mechanical energy is conserved when rolling resistance is negligible.

Experiment with the Module

Open the Rolling Without Slipping interactive tool to compare shapes, radii, drops, and incline angles:

1. Set Shape to "Solid cylinder", Radius R to "1/2", Vertical drop h to "1/2", and Incline angle degrees to "30". Verify that translational energy is 3.33333333333 J and rotational energy is 1.66666666667 J.
2. Change Shape to "Hoop" with Radius R set to "1" and Vertical drop h set to "1". Because κ = 1, translational and rotational kinetic energy split equally at 5 J each.
3. Change Radius R between "1/2", "1", and "2" for a fixed shape and drop. Observe that center speed and energies stay constant while angular speed scales inversely with R.
4. Set Vertical drop h to "0". The center speed and kinetic energies are zero at the release instant, whereas down-slope acceleration and static friction remain nonzero.