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Momentum and Angular Momentum

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Consider a small frictionless puck perched at the top of a fixed sphere of radius R. If the puck is given a tiny nudge so that is begins to slide down, through what vertical hight will it descend before it leaves the surface of the sphere?[Hint: Use conservation of energy to find the puck's speed as a function of its height, then use Newton's second law to find the normal force of the sphere on the puck. At what value of this normal force does the puck leave the sphere?]

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Consider a small frictionless puck perched at the top of a fixed sphere of radius R. If the puck is given a tiny nudge so that is begins to slide down, through what vertical hight will it descend before it leaves the surface of the sphere?[Hint: Use conservation of energy to find the puck's speed as a function of its height, then use Newton's second law to find the normal force of the sphere on the puck. At what value of this normal force does the puck leave the sphere?]

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A thin uniform rod of length .6m and mass M is rotating horizontally at 79.0 rad/s counterclockwise about an axis through its center. A particle of mass M/3 and speed 38.5 m/s hits the rod and sticks. The particle's path is perpendicular to the rod at the instant of the hit, at a distance d from the rod's center.

At what value of d are the rod and the particle stationary after the hit?

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