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A pulley of mass ? and radius ? (? = 1 2 ?? 2 ) is...

A pulley of mass ? and radius ? (? = 1 2 ?? 2 ) is free to rotate around its fixed axis without friction. A spider of mass ? falls vertically (starting with zero initial velocity) from a point on the ceiling which is a height ℎ above and a distance ? to the right of the center of the pulley (Figure on the left). The spider holds on to the pulley as soon as it hits, and the pulley and the spider start rotating. Gravitational acceleration is g. (a) (5 Pts.) What is the speed of the spider just before it hits the pulley? (b) (5 Pts.) What is the angular speed of the pulley with the spider on it just after the collision? (c) (5 Pts.) Find the angular velocity of the pulley at the time the spider reaches the bottom of the pulley. (d) (5 Pts.) How much energy is lost during the collision?

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