Question

What if i have a system consisting a rod with 2 balls with same mass at both of the end, if a third ball fall into one of the balls on the rod with a speed v and mass m, suppose the third ball stick to the one of the balls,how does the linear momentum of the third ball transfer to the system angular momentum?

Answer 1

The third ball's linear momentum creates a torque that spins the rod, converting to angular momentum.

Step-by-step explanation:

When a third ball with mass m and speed v collides and sticks to one of the balls at the end of the rod, the linear momentum of the third ball is converted into the system's angular momentum. Since linear momentum is a vector quantity, its direction relative to the pivot point of the rod matters for this conversion.

The formula for angular momentum (L) concerning the pivot point is L = r × p, where r is the distance from the pivot to the point where the third ball hits and p is the linear momentum of the third ball. By sticking to the ball at the end of the rod, the linear momentum creates a torque that causes the system to spin, conserving angular momentum.