BackCalculate the moment of inertia of the array of point objects shown in Fig. 10–58 about the y axis, and the x axis. Assume m = 22kg, M = 3.2kg, and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the x axis. About which axis would it be harder to accelerate this array?
A dad pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 330 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. What force is required at the edge?
A solid ball is released from rest and slides down a hillside that slopes downward at 65.0° from the horizontal. In part (a), why did we use the coefficient of static friction and not the coefficient of kinetic friction?
A solid uniform disk of mass 21.0 kg and radius 85.0 cm is at rest flat on a frictionless surface. Figure 10–76 shows a view from above. A string is wrapped around the rim of the disk and a constant force of 35.0 N is applied to the string. The string does not slip on the rim. When the cm has moved a distance of 5.2 m, determine how fast the disk is spinning (in radians per second.
(II) A potter is shaping a bowl on a potter’s wheel rotating at constant angular velocity of 1.6 rev/s (Fig. 10–59). The friction force between her hands and the clay is 1.8 N total. How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hands? The moment of inertia of the wheel and the bowl is 0.11 kg m².
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(II) A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0.380 kg. Calculate the applied torque needed to accelerate it from rest to 1950 rpm in 5.00 s. Take into account a frictional torque that has been measured to slow down the wheel from 1500 rpm to rest in 55.0 s.