Question

A rod of mass M and length L floats motionless in space. A piece of putty travels towards the rod with velocity v and attaches perpendicularly at a distance r from the center of the rod. How fast is the rod-putty system rotating angularly and translating linearly after the collision?

Answer 1

(Assume uniform rod density.)

Answer 2

You also need the mass of the putty, I'll refer to it as m here.

Both linear and angular velocity are conserved. Initial angular velocity is \[L=m*r*v\]The final angular momentum is \[L=I *\omega\]
Where I is the momentum of inertia of the rod and putty together.
\[I=1/12*M*L^2+m*r^2\]
*Note, this moment of inertia equation assumes the rod will rotate about its center, which isn't actually true but is good enough for most physics classes. If you need to be more exact then solve for the new center of mass of the system and use the parallel axis theorem.

Linear momentum is easier
\[m*v=(m+M)*v_f\]

Answer 3

That was supposed to say momentum, not velocity at the top