(II) A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.
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- (II) Suppose our Sun eventually collapses into a white dwarf,losing about half its mass in the process, and winding upwith a radius 1.0% of its existing radius. Assuming the lostmass carries away no angular momentum, (a) what would theSun’s new rotation rate be? Take the Sun’s current period tobe about 30 days. (b) What would be its final kinetic energyin terms of its initial kinetic energy of today?(II) A uniform disk turns at 3.3 rev/s around a frictionless central axis. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter, is dropped onto the freely spinning disk, Fig. 8–56. They then turn together around the axis with their centers superposed. What is the angular frequency in rev/s of the combination? FIGURE 8-56 Problem 72.(II) A potter is shaping a bowl on a potter's wheel rotating at constant angular velocity of 1.6 rev/s (Fig. 8–48). The friction force between her hands and the clay is 1.5 N total. (a) How large is her torque on the wheel, if the diameter of the bowl is 9.0 cm? (b) 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. FIGURE 8–48 Problem 40.
- A 4.00-kg mass and a 3.00-kg mass are attached to opposite ends of a very light 42.0-cm-long horizontal rod (Fig. 8–61). The system is rotating at angular speed w = 5.60 rad/s about a vertical axle at the center of the rod. Determine (a) the kinetic energy KE of the system, and (b) the net force on each mass. 3.00 kg 4.00 kg FIGURE 8-61 Problem 87.A child of mass m stands at the center of a merry-go-round with moment of inertia Io and radius R that can rotate freely about a frictionless axle at its center. A group of her friends spins it up to an angular velocity wo counterclockwise while she stands at the center. The child then walks to the edge of the merry-go-round. (i) What is the angular velocity of the merry-go-round when she reaches the edge? (ii) If she then jumps off with speed vo at the angle 0, what is the final angular velocity of the merry-go-round? Law Application R (overhead view) 0 VO(II) A small 350-gram ball on the end of a thin, light rodis rotated in a horizontal circle of radius 1.2 m. Calculate(a) the moment of inertia of the ball about the center ofthe circle, and (b) the torque needed to keep the ballrotating at constant angular velocity if air resistance exertsa force of 0.020 N on the ball. Ignore air resistance onthe rod and its moment of inertia.