# Conservation laws – Ball hitting a rod about its end

**1. The problem statement, all variables and given/known data**

**2. Relevant equations**

v = wr

K_total = 1/2Mv^2 + 1/2Iw^2

L = Iw

p = mv

**3. The attempt at a solution**

a. No friction or other outside forces are acting on the system, so linear momentum is conserved.

The collision is elastic, so kinetic energy is conserved.

There are no external torques so angular momentum is also conserved.

b. We can now write our conservation laws:

Linear momentum: Mv_0 = Mv_f + Mv_f

Energy: 1/2Mv_0^2 = 1/2Mv_f^2 + 1/2Iw_f^2

Angular momentum: MRv_0 = Iw + MRv_f

Is my thinking correct so far?

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