Solve Rigid Body Collision: System Approach w/Cons. Angular Momentum

[anandvineet27]

under what conditions can a rigid body collision problem be solved using a system approach, (i.e by using the conservation of angular momentum of the two rigid bodies about some point)
the equation M=d[H]/dt is only valid when M and H are taken about a point fixed in a massless extension of a rigid body or its mass center. Yet for two-body collision problems, I have seen the total angular momentum being conserved about some point,( say, if a ball collides with a rod, then the cg of the rod).Is this approach valid?

 

[tiny-tim]

welcome to pf!

hi anandvineet27! welcome to pf!

torque = rate of change of angular momentum (τ = dL/dt) is valid about any axis

(however, τ = Iα is valid only for an axis through the centre of mass or centre of rotation)

 

[anandvineet27]

only valid about axes fixed in an inertial space.

 

[tiny-tim]

yes

 

[PJC01]

The system approach with conservation of angular momentum can be used to solve a rigid body collision problem when certain conditions are met. These conditions include the conservation of mass, the conservation of energy, and the conservation of angular momentum about a fixed point.

In order for the equation M=d[H]/dt to be valid, the point about which the angular momentum is taken must be fixed in a massless extension of the rigid body or at its mass center. This means that the point must be stationary and not part of the rigid body itself.

In the case of a two-body collision problem, the total angular momentum can be conserved about a point that is not the mass center of either body. This approach is valid as long as the point chosen is fixed and not part of either body. For example, in the case of a ball colliding with a rod, the center of gravity of the rod can be used as the fixed point for conservation of angular momentum. This is because the center of gravity is a fixed point in space and is not part of either the ball or the rod.

In summary, the system approach with conservation of angular momentum can be used to solve a rigid body collision problem when the conservation of mass, energy, and angular momentum about a fixed point are all taken into account. The choice of the fixed point for conservation of angular momentum depends on the specific problem and should be a point that is not part of either body involved in the collision.