# Rotational dynamics about a point or an axis?

In several books and sites, it is written that torque is calculated about an axis, and angular momentum is calculated about a point. In MIT's Angular momentum lecture pdf, Angular momentum has been calculated about a point and then this has been used to calculate the torque about that point.

In this page, it has been explicitly mentioned that angular momentum is defined about a point in an inertial frame.

On some other websites, it was mentioned that torque is defined about a point and each point determines a unique axis in itself, about which the torque is the same for every point on that axis. Is this true? For central axes?

Which is true? Is torque calculated about a point or an axis? Is angular momentum calculated about a point or an axis? If torque and angular momentum are not defined in the same sense, then how can they be linked to Newton's equations (maybe due to the axial property of moment of inertia?)?

• You can calculate torque about each of three (orthogonal) axes, if that makes this clearer. Angular momentum needs to be based on an origin but you, again, could think of it as the values about each of 3 axes. Dec 14, 2014 at 16:22
• So, point or plane? Or both are the same? Dec 14, 2014 at 16:59

The discussion is mostly semantic. They are both calculated relative to a point, in the case of the torque the point has the additional meaning that if you put an axle trough the point, the object will start to rotatte around it if the net torque is not zero. It happens also that the torque will be the same if you chose any other point along the axis (axel).

• Like I said. :-) Dec 14, 2014 at 16:25
• @CarlWitthoft yes, we wrote both simultaneously :)
– user65081
Dec 14, 2014 at 16:27
• OMG: we've disproven the Special Relativity rules about simultaneity! Dec 14, 2014 at 16:28
• @CarlWitt I just realized that your comment was written 12 minutes before my answer, I wasnt aware.
– user65081
Dec 14, 2014 at 16:32
• So does the choice of the point determine a unique axis? Dec 14, 2014 at 16:57

Well for a rotation the reference taken is the axis not a point as for any system of particles, given a point, it can be rotated in many different ways so to define a unique rotation you choose an axis, and that applies to both angular momentum and torque. But let's say you want to calculate the angular momentum of the earth as it is rotating and simultaneously revolving, so both motions would contribute to angular momentum and for the revolution part the angular momentum would be defined about a point but the one associated with rotation would be defined about the axis.