1. Analogies exist between rotational and translational physical quantities. Ide

Question

1. Analogies exist between rotational and translational physical quantities. Identify the rotational term analogous to each of the following: acceleration, force, mass, work, translational kinetic energy, linear momentum, impulse.

2. A ball slides up a frictionless ramp. It is then rolled without slipping and with the same initial velocity up another frictionless ramp (with the same slope angle). In which case does it reach a greater height, and why?

3. A ball with an initial velocity of 8.00 m/s rolls up a hill without slipping. Treating the ball as a spherical shell, calculate the vertical height it reaches. (b) Repeat the calculation for the same ball if it slides up the hill without rolling.

Explanation / Answer

KEi = PEf

1/2 I w2 = m g h

(1/2)(2/3 * m r2) w2 = m g h

h(1/3) v2 / g = 1/3 * 8.002 / 9.8

= 2.18 m

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