Is the value of the work done by the forces acting on a rigid body frame dependent?

Question

I was going through the definition of "Work of Forces Acting on a Rigid Body" in Wikipedia .

Here they have mentioned that work done can be calculated by taking any reference point on the body and calculating the work done by the net torque of forces (and pseudo forces) in rotating the body about the reference point and the work done by net force (including pseudo forces) in displacing the reference point (in an inertial frame).

My doubts here are:

1. Is the total work done (by the torque and the force) is same no matter where the reference point is chosen?

2. If point 1 is true, then what does this imply for Work Energy Theorem provided that the Kinetic Energy is frame dependent?

Answer 1

By reference point, they don't mean reference frame.

The proof is based around keeping track of the motion of one point on the body. Using the rotation matrix $[A(t)]$, based on that one point, you can determine the motion of any other point on the body. This reference point does not need to be anything specific, since for any point you choose, there is a rotation matrix that will allow you to track the motion of all other points.

As you know, kinetic energy is indeed frame-dependent. If you switched reference frames, then your KE would change. However, that's not what this proof called for. Work-KE theorem applies as expected.

Answer 2

you are confusing reference point and reference frame, in a particular frame of reference any point taken as the reference point in that frame, will have the total work done same but as the frame is accelerating we have to consider the work done by pseudo force as well.