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# Conservation of momentum

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A hockey stick of mass m_s and length L is at rest on the ice (which is assumed to be frictionless). A puck with mass m_p hits the stick a distance D from the middle of the stick. Before the collision, the puck was moving with speed v° in a direction perpendicular to the stick. The collision is completely inelastic, and the puck remains attached to the stick after the collision.

a)Find the speed v_f of the center of mass of the stick+puck combination after the collision

b)After the collision, the stick and puck will rotate about their combined center of mass. How far is this center of mass from the point at which the puck struck? In the figure, this distance is (D-b)

c)What is the angular momentum L_cm of the system before the collision, with respect to the center of mass of the final system?

d)What is the angular velocity w of the stick+puck combination after the collision? Assume that the stick is uniform and has a moment of inertia I_o about its center. Your answer for w should not contain the variable b.

e)Which of the following statements are TRUE?

1) Kinetic energy is conserved.
2) Linear momentum is conserved.
3) Angular momentum of the stick+puck is conserved about the center of mass of the combined system.
4) Angular momentum of the stick+puck is conserved about the (stationary) point where the collision occurs.

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The solution contains 5 pages of derivations and diagrams that deals with conservation of angular momentum and motion about the center of mass.

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