Chapter 12: Q. 34 (page 331)
A 500g, 8-cm-diameter can is filled with uniform, dense food. It rolls across the floor at 1.0 m/s. What is the can's kinetic energy?
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A satellite follows the elliptical orbit shown in FIGURE P12.77. The only force on the satellite is the gravitational attraction of the planet. The satellite’s speed at point a is 8000 m/s.
a. Does the satellite experience any torque about the center of the planet? Explain.
b. What is the satellite’s speed at point b?
c. What is the satellite’s speed at point c?
A kg ball on the end of a lightweight rod is located at where the axis is vertical. The other end of the rod is attached to a pivot at . What is the torque about the pivot? Write your answer using unit vectors.
A rod of length L and mass M has a nonuniform mass distribution. The linear mass density (mass per length) is λ= 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.
Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of a playground merry-go-round with his arms extended, holding a 4.0 kg dumbbell in each hand. The merry-go-round can be modeled as a 4.0-m-diameter disk with a weight of 1500 N. Luc’s body can be modeled as a uniform 40-cm-diameter cylinder with massless arms extending to hands that are 85 cm from his center. The merry-go-round is coasting at a steady 35 rpm when Luc brings his hands in to his chest. Afterward, what is the angular velocity, in rpm, of the merry-go-round?
The two blocks in FIGURE CP12.86 are connected by a massless rope that passes over a pulley. The pulley is 12 cm in diameter and has a mass of 2.0 kg. As the pulley turns, friction at the axle exerts a torque of magnitude 0.50 N m. If the blocks are released from rest, how long does it take the 4.0 kg block to reach the floor?
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