Describing the circle of a uniform rod hit at one end

[schaafde]

I have a uniform rod laying on a table. A ball comes in and hits the rod making it move backwards but also rotating. Assuming that we are in a frictionless environment, how do describe the circle made by the rod?

 

[K^2]

Circle made by rod?

The ball will transfer linear and angular momentum to the rod. While we don't know the exact time-profile of the impact force, we know that torque = force * arm at any given moment. Arm, in this case, is the distance from rod's center of mass to the point of impact. That means that after collision rod's angular momentum = arm * linear momentum. Using moment of inertia for rod you should easily be able to find the ratio between rod's linear and angular velocities from that.

 

[schaafde]

yes if the ball hit the bat and the bat rotated around in a circular motion. How would i describe that circle?

 

[K^2]

A circle only has one parameter - radius. You're not making a whole lot of sense.

 

[schaafde]

I understand that but the radius should be longer than the length of the bat because the bat is not pinned at one end. Therefore the center of the circle isn't at the end of the bat. I guess I am asking where is the center of the circle and how would I calculate that new radius.

 

[K^2]

Center of the circle is at the center of mass. The center of mass of a body, when no external force is applied, can only move in a straight line. Everything else rotates around the center of mass.