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Chapter 8: 8-6MCQ (page 198)
Two spheres have the same radius and equal mass. One sphere is solid, and the other is hollow and made of a denser material. Which one has the bigger moment of inertia about an axis through its center?
(a) The solid one.
(b) The hollow one.
(c) Both the same.
The correct option is (b).
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A centrifuge rotor rotating at 9200 rpm is shut off and eventually brought uniformly to rest by a frictional torque of \({\bf{1}}{\bf{.20}}\;{\bf{m}} \cdot {\bf{N}}\). If the mass of the rotor is 3.10 kg, and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest, and how long will it take?
A merry-go-round with a moment of inertia equal to \({\bf{1260}}\;{\bf{kg}} \cdot {{\bf{m}}{\bf{2}}}\) and a radius of 2.5 m rotates with negligible friction at \({\bf{1}}{\bf{.70}}\;{{{\bf{rad}}} \mathord{\left/ {\vphantom {{{\bf{rad}}} {\bf{s}}}} \right. \\{\bf{s}}}\). A child initially standing still next to the merry-go-round jumps onto the edge of the platform straight toward the axis of rotation, causing the platform to slow to \({\bf{1}}{\bf{.35}}\;{{{\bf{rad}}} \mathord{\left/{\vphantom {{{\bf{rad}}} {\bf{s}}}} \right.
\\{\bf{s}}}\). What is her mass?
The moment of inertia of a rotating solid disk about an axis through its CM is \(\frac{{\bf{1}}}{{\bf{2}}}{\bf{M}}{{\bf{R}}^{\bf{2}}}\) (Fig. 8鈥�20c). Suppose instead that a parallel axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller? Explain why.
If you used 1000 J of energy to throw a ball, would it travel faster if you threw the ball (ignoring air resistance)
(a) so that it was also rotating?
(b) so that it wasn't rotating?
(c) It makes no difference.
A person exerts a horizontal force of 42 N on the end of a door 96 cm wide. What is the magnitude of the torque if the force is exerted (a) perpendicular to the door and (b) at a 60.0掳 angle to the face of the door?
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