Chapter 9: Q2Q (page 376)
Can you give an example of a system that has no atoms located at its center of mass?
A hoop is a system that has no atoms located at its center of mass.
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Consider the acceleration of a car on dry pavement, if there is no slipping. The axle moves at speed v, and the outside of the tire moves at a speed relative to the axle. The instantaneous velocity of the bottom of the tire is zero. How much work is done by the force exerted on the tire by the road? What is the source of the energy that increases the carโs translational kinetic energy?
Question: Under what conditions does the energy equation for the point particle system differ from the energy equation for the extended system? Give two examples of such a situation. Give one example of a situation where the two equations look exactly alike.
A solid uniform-density sphere is tied to a rope and moves in a circle with speed . The distance from the center of the circle to the center of the sphere is , the mass of the sphere is , and the radius of the sphere is . (a) What is the angular speed ? (b) What is the rotational kinetic energy of the sphere? (c) What is the total kinetic energy of the sphere?
A cylindrical rod of uniform density is located with its center at the origin, and its axis along the x axis. It rotates about its center in the xy plane, making one revolution every 0.03 s. rod has a radius of 0.08 m, length of 0.7 m, and mass of 5 kg. It makes one revolution every 0.03 s. What is the rotational kinetic energy of the rod?
Determine the location of the center of mass of an L-shaped object whose thin vertical and horizontal members have the same length Land the same mass M. Use the formal definition to find the x and ycoordinates, and check your result by doing the calculation with respect to two different origins, one in the lower left corner at the intersection of the horizontal and vertical members and at the right end of the horizontal member.
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