Conservation of Energy with Rotation Video Lessons

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Problem: A solid cylinder with moment of inertia I = 1/2 MR2, a hollow cylinder with moment of inertia I = MR2 and a solid sphere with moment of inertia I = 2/5 MR2 all have a uniform density, the same mass and the same radius. They are placed at the top of an inclined plane and allowed to roll down the inclined plane without slipping. Rank them in order of total kinetic energy at the bottom of the incline, from higher to lower.[a] sphere(1st), hollow cylinder(2nd), solid cylinder(3rd)[b] sphere(1st), solid cylinder(2nd), hollow cylinder(3rd)[c] hollow cylinder(1st), sphere(2nd), solid cylinder(3rd)[d] hollow cylinder(1st), solid cylinder(2nd), sphere(3rd)[e] they all have the same kinetic energy

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Problem Details

A solid cylinder with moment of inertia I = 1/2 MR2, a hollow cylinder with moment of inertia I = MR2 and a solid sphere with moment of inertia I = 2/5 MR2 all have a uniform density, the same mass and the same radius. They are placed at the top of an inclined plane and allowed to roll down the inclined plane without slipping. Rank them in order of total kinetic energy at the bottom of the incline, from higher to lower.

[a] sphere(1st), hollow cylinder(2nd), solid cylinder(3rd)

[b] sphere(1st), solid cylinder(2nd), hollow cylinder(3rd)

[c] hollow cylinder(1st), sphere(2nd), solid cylinder(3rd)

[d] hollow cylinder(1st), solid cylinder(2nd), sphere(3rd)

[e] they all have the same kinetic energy

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What scientific concept do you need to know in order to solve this problem?

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

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Based on our data, we think this problem is relevant for Professor Galeazzi's class at UM.