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Chapter 10: Problem 40
A rolling ball has total kinetic energy \(100 \mathrm{J}, 40 \mathrm{J}\) of which is rotational energy. Is the ball solid or hollow?
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A thin rod of length \(L\) and mass \(M\) is free to pivot about one end. If it makes an angle \(\theta\) with the horizontal, find the torque due to gravity about the pivot. (Hint: Integrate the torques on the mass elements composing the rod.)
A 55 -g mouse runs out to the end of the 17 -cm-long minute hand of a grandfather clock when the clock reads 10 past the hour. What torque does the mouse's weight exert about the rotation axis of the clock hand?
A compact disc (CD) player varies the rotation rate of the disc in order to keep the part of the disc from which information is being read moving at a constant linear speed of \(1.30 \mathrm{m} / \mathrm{s}\) Compare the rotation rates of a 12.0 -cm-diameter CD when information is being read (a) from its outer edge and (b) from a point \(3.75 \mathrm{cm}\) from the center. Give your answers in \(\mathrm{rad} / \mathrm{s}\) and rpm.
Two forces act on an object, but the net force is zero. Must the net torque be zero? If so, why? If not, give a counterexample.
A solid sphere and a solid cube have the same mass, and the side of the cube is equal to the diameter of the sphere. The cube's rotation axis is perpendicular to two of its faces. Which has greater rotational inertia about an axis through the center of mass?
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