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.

🤓 Based on our data, we think this question is relevant for Professor Lockett-Ruiz's class at CSUF.

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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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Our tutors have indicated that to solve this problem you will need to apply the Energy of Rolling Motion concept. You can view video lessons to learn Energy of Rolling Motion. Or if you need more Energy of Rolling Motion practice, you can also practice Energy of Rolling Motion practice problems.

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What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Lockett-Ruiz's class at CSUF.