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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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An oxygen molecule consists of two oxygen atoms whose total mass is \({\bf{5}}{\bf{.3 \times 1}}{{\bf{0}}^{{\bf{ - 26}}}}\;{\bf{kg}}\) and the moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is \({\bf{1}}{\bf{.9 \times 1}}{{\bf{0}}^{{\bf{ - 46}}}}\;{\bf{kg}} \cdot {{\bf{m}}^{\bf{2}}}\). From these data, estimate the effective distance between the atoms.
Calculate the moment of inertia of an align of point objects, as shown in Fig. 8鈥�47 about (a) the y axis and (b) the x-axis. Assume two masses, \(m = 2.2\;{\rm{kg}}\)and \(M = 3.4\;{\rm{kg}}\), and the objects are wired together by very light, rigid pieces of wire. The align is rectangular and split through the middle by the x-axis. (c) About which axis would it be harder to accelerate this align?
FIGURE 8-47
Problem 39
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?
A solid sphere of a 0.72 m diameter can be rotated about an axis through its center by a torque, which accelerates it uniformly from rest through a total of 160 revolutions in 15.0 s. What is the mass of the sphere?
(a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.013 m. Use conservation of energy to calculate the linear speed of the yo-yo just before it reaches the end of its 1.0-m-long string, if it is released from rest. (b) What fraction of its kinetic energy is rotational?
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