Physics HL · Chapter 5: Rigid Body Mechanics
5.4 Rolling Without Slipping
Model rolling as linked translation and rotation and explain how energy partitions during descent.
Estimated time: 22 minutes
The No-Slip Constraint
Rolling without slipping links center-of-mass speed and angular speed through v_cm = omega R. This relation is kinematic and must be applied alongside dynamics or energy principles. It does not mean friction is absent; rather, static friction enforces the no-slip condition without dissipating energy through sliding.
Energy Sharing in Rolling Systems
As a rolling object descends, gravitational potential energy converts into translational kinetic energy of the center of mass and rotational kinetic energy about the center. Objects with larger moment of inertia for the same mass and radius place a larger fraction of energy into rotation and therefore gain less translational speed at the same height drop.
This explains a standard race result: on the same incline, a solid sphere usually reaches the bottom before a hoop, even if mass and radius are comparable. The sphere has lower rotational inertia relative to its mass-radius scale.
When the No-Slip Condition Fails
If available static friction is insufficient, the contact point slides and v_cm = omega R no longer holds. At that stage, kinetic friction dissipates mechanical energy and the simple rolling formulas must be replaced by a slip model with frictional work losses.