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(23) Work and Power- Rotations

# (23) Work and Power- Rotations - Lecture 23 Work and power...

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Lecture 23 Work and power for rotations. Examples.

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ACT: Heavy (real) pulleys Two blocks of masses m 1 and m 2 (> m 1 ) are connected through a string that goes through two different pulleys. Pulley 1 is made of plastic. Pulley 2 is made of iron. In both cases, m 1 is initially at rest on the floor and m 2 hangs at distance h from the floor. Both systems are released simultaneously. In which case does mass m 2 hit the floor first? A. Case 1 B. Case 2 C. Same for both Case 1 (plastic) Case 2 (iron) m 2 m 1 m 2 m 1
Case 1 (plastic) Case 2 (iron) m 2 m 1 m 2 m 1 Rotational kinetic energy of the pulley: 2 2 2 1 1 2 4 rot KE I MR ϖ ϖ = = 2 cylinder 1 2 I MR = In case 2, the rotation of the pulley absorbs a larger fraction of the energy available.

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2 2 2 2 2 1 2 1 1 1 1 1 0 2 2 2 2 m gh mv mv MR m gh ϖ + = + + + h v v ϖ If string doesn’t slip on pulley: v = R ϖ ( 29 2 2 1 1 2 1 2 2 M m m gh m m v - = + + m 2 m 1 h R ( 29 2 1 1 2 2 2 m m gh v M m m - = + +
Work done by a torque (for pure rotations) Work from θ 1 to θ 2 : θ τ θ θ d W z = 2 1 θ τ = z W If torque is constant, A force F acts on an object as it rotates from θ 1 to θ 2 .

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