Question

So, I was reading my textbook in the section regarding net torque, and they gave an example of a seesaw with one person at each end, and they said that there is a net external torque due to the force of gravity on each person. I completely understand that; however, when I was reading another section of my textbook, they were talking about the conservation of angular momentum, which only happens when the net torque is zero. So they gave an example of a circular disk that rotates freely in a horizontal plane about a frictionless, verticle axle. On top of that, there is a person who walks slowly from the rim of the disk towards the center. The textbook modeled this problem as conservation of angular momentum problem, but why? Isn't the weight of the person causing an external torque just how the weight of the two people in the seesaw caused a net external torque?

Answer 1

The thing is the Angular momentum is a vector quantity and in a 3 dimensional space it has three independent components (three perpendicular directions x, y and z)(similarly torque also has three components), Hence we can apply Conservation of angular momentum independently across the three independent components if the torque is zero in all the three components. In other words we can say that, if the torque is about the axis, about which the rotation takes place then we can't apply Conservation law in that axis. In the Seesaw case, the torque was about the same axis as about which the see saw rotated. (The forces affected the rotation).

But, In the case where disk is rotating and a person is walking towards the center. The gravitational force due to the person does not generate torque about the axis about which it rotates. Hence we can take Conservation Law in the axis of rotation.

(In this case the axis of rotation is perpendicular to the disk, whereas the torque generated due to the weight is on the plane of the disk and is perpendicular to the axis of rotation).