# Translational vs rotational momentum

#### Yaridovich

Suppose I am floating in space and have a thin rod oriented vertically floating in front of me. This rod has its center of mass in the center of the rod (uniform mass distribution) and is not fixed to anything. I then throw a point particle with non-negligible mass horizontally;it hits the rod near one of its ends and an elastic collision occurs. How much of the point particle's momentum is transferred to the rod as translational momentum as opposed to angular momentum?

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#### graphene

particle - mass m, rod - mass M, length L,

before collision, particle velocity v. rod at rest
after collision, particle velocity v1, rod - translational velocity v2, rotational velocity w.

conserve linear & angular momentum, & energy,

linear momentum : mv = mv1 + Mv2

angular momentum : mvL/2 = mv1*L/2 + Iw. I = mL^2 / 12

energy : mv^2 = mv1^2 + Mv2^2 + Iw^2.

elimiate v1 & calculate Mv2 / mv and Iw / mv

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