09_InstSolManual_PDF_Part15

09_InstSolManual_PDF_Part15 - Rotational Motion 9-15(b Now...

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(b) Now the initial potential energy is converted to both translational and rotational kinetic energy as the stone rolls down the hill: so and This gives and (c) In (a) all the initial gravitational potential energy is converted back to final gravitational potential energy; the kinetic energy at the final maximum height is zero. In (b) the stone gains rotational kinetic energy as it rolls down the hill and it still has this rotational kinetic energy at its maximum height; not all the initial potential energy is converted into the final potential energy. Reflect: Both answers do not depend on the mass or radius of the stone. But the answer to (b) depends on how the mass is distributed; the answer would be different for a hollow rolling sphere. 9.70. Set Up: Use conservation of energy, to find the speed of the ball just as it leaves the top of the cliff. Let at the bottom of the cliff, so and Rolling without slipping gives Consider the projectile motion of the ball after it goes over the cliff to find its horizontal range and final speed.
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