Chapter 8: 8-13MCQ (page 198)
Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, your angular velocity will
(a) increase.
(b) decrease.
(c) stay the same.
The correct option is (c).
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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 laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges at an angle \({\bf{\theta }}\) (Fig. 8–40) of \({\bf{1}}{\bf{.4 \times 1}}{{\bf{0}}^{{\bf{ - 5}}}}\;{\bf{rad}}\). What diameter spot will it make on the Moon?
FIGURE 8-40 Problem 3.
A hollow cylinder (hoop) is rolling on a horizontal surface at speed v = 3.0 m/s when it reaches a 15° incline. (a) How far up the incline will it go? (b) How long will it be on the incline before it arrives back at the bottom?
(II) Estimate the kinetic energy of the Earth with respect to the Sun as the sum of two terms, (a) that due to its daily rotation about its axis, and (b) that due to its yearly revolution about the Sun. (Assume the Earth is a uniform sphere with\({\bf{mass}} = {\bf{6}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{24}}}}{\bf{ kg}}\),\({\bf{radius}} = {\bf{6}}{\bf{.4 \times 1}}{{\bf{0}}^{\bf{6}}}{\bf{ m}}\)and is\({\bf{1}}{\bf{.5 \times 1}}{{\bf{0}}^{\bf{8}}}{\bf{ km}}\)from the Sun.)
A small solid sphere and a small thin hoop are rolling along a horizontal surface with the same translational speed when they encounter a 20° rising slope. If these two objects roll up the slope without slipping, which will rise farther up the slope?
(a) The sphere.
(b) The hoop.
(c) Both the same.
(d) More information about the objects' mass and diameter is needed.
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