Question

Chapter 11, Problem 081 A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center (see the figure). The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg-m2. The wheel is initially at rest at the top of a surface that is inclined at angle 58.4° with the horizontal; the axle rests on the surface while the wheel extends into a groove in the surface without touching the surface. Once released, the axle rolls down along the surface smoothly and without slipping. When the wheel-axle combination has moved down the surface by 1.94 m, what are (a) its rotational kinetic energy and (b) its translational kinetic energy? Wheel Axle Groove (a) Number Units (b) Number Units

Answer 1

A)

mgd sin(theta) = 0.5 mr^2w^2 + I w^2

10 x 9.8 x 1.94 sin(58.4) = 0.5 x 10 x w^2 x 0.2^2 + 0.5 x 0.6 x w^2

161.93 = 0.5 w^2

w = 18 rad/sec

KE = 0.5 x 0.6 x 18^2 = 97.16 J

B)

KE = (10 x 9.8 x 1.94 sin(58.4)) - 97.16 = 64.77 J

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