Which item reaches the bottom of its ramp first?
Answer: The block slides down without friction. All the gravitational potential energy it gains is turned into translational kinetic energy. 0.5 * M * v^2 = GPE 2 * GPE v^2 = ------- M The ball rolls down. Some of the gravitational potential energy energy is turned into translational kinetic energy, but some is turned into rotational kinetic energy. Thus, it has less translational kinetic energy, and so must be moving more slowly. 0.5 * M * v^2 + 0.5 * I * (omega)^2 = GPE 2 * GPE - (I * omega^2) v^2 = ----------------------- M So the ball is moving more slowly.
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