Can conservation of linear or angular momentum be used to simplify the kinetics in this problem? If so, which would be more preferred in a problem like this?

Mason: You need to first consider IF linear momentum or IF angular momentum is conserved. How do you do this? Look at your FBD.

Say you consider a combined FBD of the bar and the bullet.

If there are external forces acting in a given direction, then linear momentum in that directions is NOT conserved. Here you should see that linear momentum is conserved in neither the x- nor the y-direction.

If the moment about a fixed point on the FBD is zero, then angular momentum about that point is conserved. Look at your FBD - all external forces act through point O. Therefore, angular momentum for the system of the bar + bullet is conserved about O.

Would the linear momentum be conserved if you consider both objects to be in the system because there is no external force? Above it says that linear momentum is not conserved if there is no force acting in that direction, but I thought momentum IS conserved when there are no forces in that direction.

What is the best method to derive the equation for theta (t)? I believe I have the correct expression for theta dot (0) and subsequent EOM equations, do you need to relate the angular velocity as an expression of time?

I made the FBD as one system with both the bullet and the bar. I think when we are using LIM or AIM it's best to include as many components into the system together similar to work energy approach. When you sum the forces about O, you can see there are no forces acting, so momentum is conserved when you consider the bullet and the bar in the system together.

Can conservation of linear or angular momentum be used to simplify the kinetics in this problem? If so, which would be more preferred in a problem like this?

Mason: You need to first consider IF linear momentum or IF angular momentum is conserved. How do you do this? Look at your FBD.

Say you consider a combined FBD of the bar and the bullet.

If there are external forces acting in a given direction, then linear momentum in that directions is NOT conserved. Here you should see that linear momentum is conserved in neither the x- nor the y-direction.

If the moment about a fixed point on the FBD is zero, then angular momentum about that point is conserved. Look at your FBD - all external forces act through point O. Therefore, angular momentum for the system of the bar + bullet is conserved about O.

Does this help?

Would the linear momentum be conserved if you consider both objects to be in the system because there is no external force? Above it says that linear momentum is not conserved if there is no force acting in that direction, but I thought momentum IS conserved when there are no forces in that direction.

Sorry. A typo from typing too fast and not proof-reading. I will fix that.

Yes, thank you!

What is the best method to derive the equation for theta (t)? I believe I have the correct expression for theta dot (0) and subsequent EOM equations, do you need to relate the angular velocity as an expression of time?

How do we make the free body diagram? I'm not sure if it's the whole system together or individually.

I made the FBD as one system with both the bullet and the bar. I think when we are using LIM or AIM it's best to include as many components into the system together similar to work energy approach. When you sum the forces about O, you can see there are no forces acting, so momentum is conserved when you consider the bullet and the bar in the system together.