A thin, uniform, metal bar, 2.5 m long and weighing 70 N. is hanging vertically

Question

A thin, uniform, metal bar, 2.5 m long and weighing 70 N. is hanging vertically from the celling by a frictionless pivot. Suddenly it is struck 1.3 m below the celling by a small 4-kg ball, initially traveling horizontally at 13 m/s. The ball rebounds in the opposite direction with a speed of 5 m/s. You may want to review Part A Find the angular speed of the bar just after the collision. Part B During the collision, why is the angular momentum conserved but not the linear momentum? Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

Explanation / Answer

a) From conservation of angular momentum

m1 v0 d = -m1 v d + 1/3 m2 L2 w

4 * 13 * 1.3 = -4 * 5 * 1.3 + (1/3 * (70/9.8) * 2.52 * w)

w = 6.29 rad/s

b) Angular momentum is conserved as there is no unbalanced torques about the pivot

linear momentum is not conserved because pivot exerts an unbalanced horizontal external force on system

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