- #1
Raphael30
- 12
- 4
Member advised to use the formatting template for all homework help requests
For a question involving a ball hitting orthogonally the bottom corner of a board held by wires, I need to calculate the angular velocity of the board and ball (collision is inelastic) right after the collision, before there's any external torque.
I can easily calculate the angular momentum L, equal to the momentum of the ball x its distance from the combined center of mass at the moment of collision. I could then find w using L=wI, but integrating the moment of inertia for a rectangular board around an axis running diagonally through sounds like it's not the simplest solution.
My question is: since w has x and y components, can I treat Lx and Ly separately and combine wx and wy afterwards? I'm guessing so, as L is a vector, but I've never done this before. Also, is there a trick similar to the parallel axes theorem to calculate I when you rotate the axis around the center of mass? Thanks!
I can easily calculate the angular momentum L, equal to the momentum of the ball x its distance from the combined center of mass at the moment of collision. I could then find w using L=wI, but integrating the moment of inertia for a rectangular board around an axis running diagonally through sounds like it's not the simplest solution.
My question is: since w has x and y components, can I treat Lx and Ly separately and combine wx and wy afterwards? I'm guessing so, as L is a vector, but I've never done this before. Also, is there a trick similar to the parallel axes theorem to calculate I when you rotate the axis around the center of mass? Thanks!