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Chapter 12: Q. 30 (page 331)
The object shown in FIGURE EX12.30 is in equilibrium. What are the magnitudes of and
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A merry-go-round is a common piece of playground equipment. A 3.0-m-diameter merry-go-round with a mass of 250 kg is spinning at 20 rpm. John runs tangent to the merry-go-round
at 5.0 m/s, in the same direction that it is turning, and jumps onto the outer edge. John鈥檚 mass is 30 kg. What is the merry-goround鈥檚 angular velocity, in rpm, after John jumps on?
A 100g ball and a 200 g ball are connected by a , 30- cm long massless, rigid rod. The balls rotate about their center of mass at 120 rpm. What is the speed of the 100 g ball?
a. A disk of mass M and radius R has a hole of radius r centered on the axis. Calculate the moment of inertia of the disk.
b. Confirm that your answer agrees with Table 12.2 when r = 0 and when r = R.
c. A 4.0-cm-diameter disk with a 3.0-cm-diameter hole rolls down a 50-cm-long, 20o ramp. What is its speed at the bottom? What percent is this of the speed of a particle
sliding down a frictionless ramp?
A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is 位= cx2, where x is measured from the center of the rod and c is a constant.
a. What are the units of c?
b. Find an expression for c in terms of L and M.
c. Find an expression in terms of L and M for the moment of inertia of the rod for rotation about an axis through the center.
In FIGURE EX12.19, what magnitude force provides net torque about the axle?
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