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## Homework Statement

In this given pole, mass is "M" and length is "L" and it is on a frictionless surface as the picture describes. "G" is the center of gravity and "I" is the inertia.

A ball with a mass of "m" comes as the picture and hits the pole with a velocity of "v" and turns the opposite side and leaves at the same velocity. Then the pole moves under both rotational and linear motions.

## Homework Equations

(a)

i. Write an equation for the momentum of the ball before the collision.

ii. Considering only the linear motion of the pole, write an equation for the velocity of the pole "V".

(b) Now consider the rotational motion.

i. If the ball hits x distance from point "G", write an equation for the angular momentum of the ball around point "G".

ii. Write an equation for the angular velocity of the pole around point "G"

## The Attempt at a Solution

(a)

i. P = mv

ii. → mv + M0 = -mv + MV

∴ V = [itex]\frac{2mv}{M}[/itex]

(b)

i. L = mvx

ii. → mvx + 0 = -mvx + Iω

∴ ω = [itex]\frac{2mvx}{I}[/itex]