Chapter 8: 8-8Q (page 198)
Can the mass of a rigid object be considered concentrated at its CM for rotational motion? Explain.
The mass of a rigid object concentrated at the center of mass would not be considered for the rotational motion.
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This book has three symmetry axes through its center, all mutually perpendicular. The book’s moment of inertia would be smallest about which of the three? Explain.
On a 12.0-cm-diameter audio compact disc (CD), digital bits of information are encoded sequentially along an outward spiraling path. The spiral starts at radius \({{\bf{R}}_{\bf{1}}}{\bf{ = 2}}{\bf{.5}}\;{\bf{cm}}\) and winds its way out to radius \({{\bf{R}}_{\bf{2}}}{\bf{ = 5}}{\bf{.8}}\;{\bf{cm}}\). To read the digital information, a CD player rotates the CD so that the player’s readout laser scans along the spiral’s sequence of bits at a constant linear speed of 1.25 m/s. Thus the player must accurately adjust the rotational frequency f of the CD as the laser moves outward. Determine the values for f (in units of rpm) when the laser is located at \({{\bf{R}}_{\bf{1}}}\) and when it is at \({{\bf{R}}_{\bf{2}}}\).
A small mass m attached to the end of a string revolves in a circle on a frictionless table top. The other end of the string passes through a hole in the table (Fig. 8–62). Initially, the mass revolves with a speed\({v_1} = 2.4\;{\rm{m/s}}\)in a circle of radius\({r_1} = 0.80\;{\rm{m}}\). The string is then pulled slowly through the hole so that the radius is reduced to\({r_2} = 0.48\;{\rm{m}}\). What is the speed,\({v_2}\), of the mass now?
Question:(II) A ball of radius rrolls on the inside of a track of radius R(see Fig. 8–53). If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping?
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