Chapter 8: Q 31P (page 198)
Estimate the moment of inertia of a bicycle wheel 67 cm in diameter. The rim and tire have a combined mass of 1.1 kg. The mass of the hub (at the center) can be ignored (why?).
The moment of inertia of the wheel is \(0.12\;{\rm{kg}}\;{{\rm{m}}^2}\).
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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?
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?
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
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.
Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, as shown in Fig. 8–46. The ball is accelerated uniformly from rest to 8.5 m/s in 0.38 s, at which point it is released. Calculate (a) the angular acceleration of the arm and (b) the force required for the triceps muscle. Assume that the forearm has a mass of 3.7 kg, and it rotates like a uniform rod about an axis at its end.
FIGURE 8-46
Problems 35 and 36
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