Physics · University
Rolling without slipping
A uniform solid cylinder rolls without slipping, so ω = v/R; both translation and rotation contribute.
Method and conditions
A uniform solid cylinder rolls without slipping, so ω = v/R; both translation and rotation contribute.
K = Mv²/2 + Iω²/2; I=MR²/2 for a solid cylinder
Worked examples
A uniform solid cylinder of mass 3 kg rolls without slipping at center-of-mass speed 14 m/s. Find its total kinetic energy. Round the final result to 4 decimal places if needed. Answer in J.
Translation contributes Mv²/2. Rotation contributes (MR²/2)(v/R)²/2 = Mv²/4. Add them.
441 J
A uniform solid cylinder of mass 30 kg rolls without slipping at center-of-mass speed 14 m/s. Find its total kinetic energy. Round the final result to 4 decimal places if needed. Answer in J.
Translation contributes Mv²/2. Rotation contributes (MR²/2)(v/R)²/2 = Mv²/4. Add them.
4410 J
Try it
A uniform solid cylinder of mass 6 kg rolls without slipping at center-of-mass speed 20 m/s. Find its total kinetic energy. Round the final result to 4 decimal places if needed. Answer in J.
A uniform solid cylinder of mass 11 kg rolls without slipping at center-of-mass speed 13 m/s. Find its total kinetic energy. Round the final result to 4 decimal places if needed. Answer in J.
Check your work
Answers and marking notes
- 1800 J
Translation contributes Mv²/2. Rotation contributes (MR²/2)(v/R)²/2 = Mv²/4. Add them.
- 1394.25 J
Translation contributes Mv²/2. Rotation contributes (MR²/2)(v/R)²/2 = Mv²/4. Add them.
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