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PHYS 221 SI Worksheet

Matching:

1. ___ I (moment of inertia) of a point A. I = Icm + md²

2. ___ Parallel-Axis Theorem B. 1/2Iω²

3. ___ Rotational Kinetic Energy C. 1/12mL²

4. ___ I of a slender rod (axis at center of mass) D. mr²

5. ___ I of solid cylinder (axis through center) E. 1/2mR²

Problems

1. Consider a thin rod of mass 5 kg uniformly distributed over a length of 2 m. If it rotates around its center of mass at an angular velocity of ω=3rad/s counter-clockwise, what is the rotational kinetic energy of the system?

2. I release a solid cylinder and a hollow cylinder of equal mass so they both roll without slipping down a 30 degree incline ramp. If the vertical height of the ramp is 4 m, which cylinder will have more translational velocity at the bottom of the ramp? (You can do this with numbers but try to think about it quantitatively.) What are the final velocity of both cylinders?

3. I release a cylinder from a height of 2 m at the top of a 60 degree ramp and it rolls without slipping. If the translational kinetic energy at the bottom is 12 J and the cylinder has a mass of 1 kg and radius 25 cm, what is the moment of inertia of the cylinder? (SI extra-credit question: what is the inner radius of the cylinder?)

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