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## Homework Statement

I have a rod of mass m and length l on a table without any kind of friction. I give it an impulse

**J**in any point of distance d from the center of the rod, parallel to the table and perpendicular to the rod.

Find the angular velocity ω and the velocity of the center of mass v

_{0}.

## Homework Equations

Moment of inertia of the rod rotating around its center: I = m l

^{2}/ 12

**L**=

**I ·**

**ω**

## The Attempt at a Solution

From the impulse theorem:

**J**= Δ

**P**=

**P'**

I can calculate ω from the angular momentum relations:

**L**=

**d**x

**J**=

**I ·**

**ω**

ω = d J / I = 12 d J / (m l

^{2}),

which is 0 if I hit the rod on its center and max if I hit it on d = l/2.

Now I fail to calculate v

_{0}:P

Thank you in advance :)

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