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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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To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets, as shown in Fig. 8–50. Suppose that the satellite has a mass of 3600 kg and a radius of 4.0 m and that the rockets each add a mass of 250 kg. What is the steady force required of each rocket if the satellite is to reach 32 rpm in 5.0 min, starting from rest?
FIGURE 8-50
Problem 45
Calculate the net torque about the axle of the wheel shown in Fig. 8–42. Assume that a friction torque of\(0.60\;{\rm{m}}\;{\rm{N}}\)opposes the motion.
A dad pushes a small hand-driven merry-go-round tangentially and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume that the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 560 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edges. Calculate the torque required to produce the acceleration, neglecting the frictional torque. What force is required at the edge?
The radius of the roll of paper shown in Fig. 8–67 is 7.6 cm and its moment of inertia is \(I = 3.3 \times {10^{ - 3}}\;{\rm{kg}} \cdot {{\rm{m}}^2}\). A force of 3.5 N is exerted on the end of the roll for 1.3 s, but the paper does not tear so it begins to unroll. A constant friction torque of \(I = 0.11\;{\rm{m}} \cdot {\rm{N}}\) is exerted on the roll which gradually brings it to a stop. Assuming that the paper’s thickness is negligible, calculate (a) the length of paper that unrolls during the time that the force is applied (1.3 s) and (b) the length of paper that unrolls from the time the force ends to the time when the roll has stopped moving
A cyclist accelerates from rest at a rate of \({\bf{1}}{\bf{.00}}\;{\bf{m/}}{{\bf{s}}^{\bf{2}}}\). How fast will a point at the top of the rim of the tire (diameter = 0.80 cm) be moving after 2.25 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — sees Fig. 8–57.]
FIGURE 8-57 Problem 79
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