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Chapter 8: 8-11Q (page 198)
Two spheres look identical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which.
The sphere with larger rotational inertia is hollow, and the smaller rotational inertia is a solid sphere.
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A spherical asteroid with radius\(r = 123\;{\rm{m}}\)and mass\(M = 2.25 \times {10^{10}}\;{\rm{kg}}\)rotates about an axis at four revolutions per day. A “tug” spaceship attaches itself to the asteroid’s south pole (as defined by the axis of rotation) and fires its engine, applying a force F tangentially to the asteroid’s surface as shown in Fig. 8–65. If\(F = 285\;{\rm{N}}\)how long will it take the tug to rotate the asteroid’s axis of rotation through an angle of 5.0° by this method?
The platter of the hard drive of a computer rotates at 7200 rpm (rpm = revolutions per minute = rev/min). (a) What is the angular velocity \(\left( {{{{\bf{rad}}} \mathord{\left/{\vphantom {{{\bf{rad}}} {\bf{s}}}} \right.} {\bf{s}}}} \right)\) of the platter? (b) If the reading head of the drive is located 3.00 cm from the rotation axis, what is the linear speed of the point on the platter just below it? (c) If a single bit requires \({\bf{0}}{\bf{.50}}\;{\bf{\mu m}}\) of length along the direction of motion, how many bits per second can the writing head write when it is 3.00 cm from the axis?
Bicycle gears: (a) How is the angular velocity\({{\bf{\omega }}_{\bf{R}}}\) of the rear wheel of a bicycle related to the angular velocity\({{\bf{\omega }}_{\bf{F}}}\)of the front sprocket and pedals? Let \({{\bf{N}}_{\bf{F}}}\) and \({{\bf{N}}_{\bf{R}}}\) be the number of teeth on the front and rear sprockets, respectively, Fig. 8–58. The teeth are spaced the same on both sprockets and the rear sprocket is firmly attached to the rear wheel. (b) Evaluate the ratio when the front and rear sprockets have 52 and 13 teeth, respectively, and (c) when they have 42 and 28 teeth.
A wheel of mass M has radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–60). The step has height h, where h < R. What minimum force F is needed?
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