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 v0.
Moment of inertia of the rod rotating around its center: I = m l2 / 12
L = I · ω
The Attempt at a Solution
From the impulse theorem:
J = ΔP = P'
I can calculate ω from the angular momentum relations:
L = d x J = I · ω
ω = d J / I = 12 d J / (m l2),
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 v0 :P
Thank you in advance :)