Energy of Rolling Motion Video Lessons

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# Problem: A cylinder with mass m, radius a, and moment of inertia with respect to the center of mass ICM = 1/2 ma2, rolls without slipping around a loop with radius R as shown in the figure. a) What is the minimum speed of the center of mass at point C (vC) for the cylinder to move around the loop without falling off? b) What is the total kinetic energy of the cylinder at point C in the case of minimum speed? c) What is the minimum speed of the center of mass necessary at point B (vB) for the cylinder to move around the loop without falling off at the top (point C)? Write your results in terms of a, R, m, and g. Check the units/dimensions for each answer.

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###### Problem Details

A cylinder with mass m, radius a, and moment of inertia with respect to the center of mass ICM = 1/2 ma2, rolls without slipping around a loop with radius R as shown in the figure.

a) What is the minimum speed of the center of mass at point C (vC) for the cylinder to move around the loop without falling off?

b) What is the total kinetic energy of the cylinder at point C in the case of minimum speed?

c) What is the minimum speed of the center of mass necessary at point B (vB) for the cylinder to move around the loop without falling off at the top (point C)?

Write your results in terms of a, R, m, and g. Check the units/dimensions for each answer.