Rigid-body rolling University Physics I · Rotational dynamics
Rolling Relay
Set a ramp height to roll spheres, cylinders and hoops through a speed gate.
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Challenge 1 of 3
Solid-sphere delivery
A solid sphere starts at rest. Set its vertical drop to meet the first speed gate.
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Reach a speed between 3.8 and 4.2 m/s at the bottom.
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Divide gravitational potential energy between translation and rotation, and explain why the moment-of-inertia factor changes the final speed.
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From the course to the controls
The physics behind the game
Divide gravitational potential energy between translation and rotation, and explain why the moment-of-inertia factor changes the final speed.
mgh = ½mv² + ½Iω²; I = κmR²; v = √[2gh/(1 + κ)]
Model assumptions. Rigid bodies start from rest and roll without slipping, with sufficient static friction on the ramp. Energy losses and rolling resistance are neglected. Static friction supplies the torque but does no work at the instantaneous contact point on a fixed ramp.