Angular Momentum versus Linear Momentum

[Alphathree33]

Let's say I have an object with mass m moving in a line with constant velocity v.

Now, let's say it collides with an object of mass M and sticks to it, causing purely rotational motion for mass M (with mass m following right along with it since it's stuck to it.)

Just imagine a ball colliding with a rod that can rotate about a fixed axis.

I know the ball has momentum mv and I know the rod has momentum Iw (intertia times angular velocity) after the collison. I can't use conservation of energy since the collison is inelastic.

Can I say simply that the linear momentum to begin with must equal the angular momentum after the collison?

i.e. mv = Iw ?

If I can't, how do I relate linear momentum to angular momentum, in general?

 

[silverpig]

You use conservation of momentum (duh). That means both types. So you'd have your:

(intial linear momentum m) + (initial angular momentum m) + (initial linear momentum M) + (initial angular momentum M) = (final linear momentum m+M) + (final angular momentum m+M)

Depending on if you've been given geometry, you may have to calculate the moment of inertia for the new combined mass.

 

[raptor13]

The momentum of the object moving in a line is equal to the angular momentum of whatever it sticks to PLUS the angular momentum of the object.


Calculate the angular momentum of the rod as you normally do (IW = m) and then add the momentum of the ball as a point mass at whatever distance it is from the axis of rotation. Set that equal to the initial momentum and solve for whatever it is you need to solve for.