Thursday, June 28, 2018

Rotational kinematics - possible and impossible spin-ups

In this first case as pictured below, an ice skater takes advantage of the conservation of angular momentum to increase rotational velocity by bringing their arms in. However, forces and torque need to be applied for this to work. The forces must also be balanced with respect to the axis of rotation, otherwise the axis would precess.

A naïve understanding of the forces and torques at play would lead one to believe that pairs skaters (or two co-rotating comet lobes) could come together and corotate quicker due to the conservation of angular momentum. That understanding would be wrong. The main issue is that in the single skater case, the force and torque is made from the outside of the centre of mass. When two co-rotating skaters pull in to each other, there is no way to exert the right forces on each other or the ensemble to torque to the higher speed required for continued co-rotation at a reduced moment of inertia.

This is the same with two co-rotating lobes of a comet or asteroid - neither gravity nor friction (at their points of contact) gives forces in the right direction to provide spin up torque.

Resultant endpoints vary depending on the reaction forces and friction, but none of them end up with the same co-rotating lobes at a faster speed and smaller net moment of inertia (or co-rotating couple at faster speed) 

No comments: