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Rolling without slipping energy
Intermediate
Total energy combines translation and rotation.
K = ½mv² + ½Iω²Rolling bodies have K = ½mv² + ½Iω² with ω = v/R. For a solid sphere, rotation takes 2/7 of the total.
A 1 kg ball at 2 m/s rolling: K = 2 + 0.8 = 2.8 J.
Static friction does no work in pure rolling.
In more detail
A rolling object without slipping has kinetic energy shared between translation and rotation. For a solid sphere, the total kinetic energy works out to 7/10 of mv², with 2/10 in rotation and 5/10 in translation.
Real-world uses
- Rolling balls on ramps are used in physics labs to measure energy sharing.
- Bowling ball designs influence how they roll and spin.
- A ball rolling down a hill shares its energy between sliding and spinning, so it reaches the bottom more slowly than a sliding block.
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Frequently asked questions
Why does a sphere roll slower than a sliding block?
Because part of its energy goes into rotation, leaving less for translation.
Does rolling need friction?
Yes, static friction at the contact point causes rolling without slipping.
Why does the rolling ball reach the bottom with less speed?
Some of the energy goes into spinning the ball, leaving less for translation.
Related topics in Work, Energy & Power
Escape from a potential well · Work in rotation · Rotational kinetic energy · Work done by gravity on incline · Heat as energy transfer · Mechanical equivalent of heat