A thin-walled, hollow sphere of mass M and radius R isfree to rotate around a vertical shaft that passes through the center ofthe sphere. Initially the sphere is at rest. A small ball of clay of thesame mass M moving horizontally at speed v grazes the surface ofthe sphere at its equator. After grazing the surface, the ball of clay ismoving at speed v/2. (a) What is the angular momentum of the ballof clay about the shaft before it grazes the surface? After it grazes thesurface? (b) What is the angular speed of the sphere after being grazedby the ball of clay? (c) What fraction of the ball of clay’s initial kineticenergy remains as the combined kinetic energy of the sphere and theball of clay?
A thin-walled, hollow sphere of mass M and radius R isfree to rotate around a vertical shaft that passes through the center ofthe sphere. Initially the sphere is at rest. A small ball of clay of thesame mass M moving horizontally at speed v grazes the surface ofthe sphere at its equator. After grazing the surface, the ball of clay ismoving at speed v/2. (a) What is the angular momentum of the ballof clay about the shaft before it grazes the surface? After it grazes thesurface? (b) What is the angular speed of the sphere after being grazedby the ball of clay? (c) What fraction of the ball of clay’s initial kineticenergy remains as the combined kinetic energy of the sphere and theball of clay?
A thin-walled, hollow sphere of mass M and radius R isfree to rotate around a vertical shaft that passes through the center ofthe sphere. Initially the sphere is at rest. A small ball of clay of thesame mass M moving horizontally at speed v grazes the surface ofthe sphere at its equator. After grazing the surface, the ball of clay ismoving at speed v/2. (a) What is the angular momentum of the ballof clay about the shaft before it grazes the surface? After it grazes thesurface? (b) What is the angular speed of the sphere after being grazedby the ball of clay? (c) What fraction of the ball of clay’s initial kineticenergy remains as the combined kinetic energy of the sphere and theball of clay?
A thin-walled, hollow sphere of mass M and radius R is free to rotate around a vertical shaft that passes through the center of the sphere. Initially the sphere is at rest. A small ball of clay of the same mass M moving horizontally at speed v grazes the surface of the sphere at its equator. After grazing the surface, the ball of clay is moving at speed v/2. (a) What is the angular momentum of the ball of clay about the shaft before it grazes the surface? After it grazes the surface? (b) What is the angular speed of the sphere after being grazed by the ball of clay? (c) What fraction of the ball of clay’s initial kinetic energy remains as the combined kinetic energy of the sphere and the ball of clay?
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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