Physics · University
Rolling without slipping · formula reference
A uniform solid cylinder rolls without slipping, so ω = v/R; both translation and rotation contribute.
Formula
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 example
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
Prerequisites and checking
Algebra, calculus and the stated physical model. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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