Question

From this answer for the question Is the energy conserved in a moving frame of reference?, I learnt that the work-energy theorem is independent of the frame of reference. But, is the theorem valid even for non inertial frames? I know that in non inertial frames we need to include inertial (pseudo or fictional) forces. Is the work done by all forces including the inertial forces equal to the change in kinetic energy?

Please note: According to this question and answer - Work associated with pseudo force, the work done by pseudo forces must be included in order to determine the total work done by all the forces. But the answer doesn't discuss about the validity of the theorem itself.
Options:

A) Yes, the work-energy theorem is valid in non-inertial frames, and the work done by all forces, including inertial forces, equals the change in kinetic energy.
B) No, the work-energy theorem does not hold in non-inertial frames due to the inclusion of inertial forces; the theorem needs modification to account for these forces.
C) The work-energy theorem is only valid in inertial frames and does not hold in non-inertial frames, even if inertial forces are considered.
D) The work-energy theorem in non-inertial frames is valid but requires excluding inertial forces from the calculation of total work for consistency.

Answer 1

The work-energy theorem is valid in non-inertial frames when inertial forces are included in the total work done on an object. The net work, including all forces, accounts for the change in kinetic energy, confirming the theorem's applicability in non-inertial frames. Therefore the correct answer is A) Yes, the work-energy theorem is valid in non-inertial frames, and the work done by all forces, including inertial forces, equals the change in kinetic energy.

Step-by-step explanation:

Is the work-energy theorem valid in non-inertial frames? The answer to this question is Yes, the work-energy theorem is indeed valid in non-inertial frames. However, it is important to consider the inertial forces that arise due to the acceleration of the non-inertial frame itself.

When analyzing the work done in non-inertial frames, one must include the work done by both real and inertial forces to determine the total work done on an object.

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy, which is expressed as:

Wnet = ΔKE

Where Wnet includes the work done by all forces, including both conservative and non-conservative forces, as well as inertial forces in a non-inertial reference frame.

The inclusion of inertial forces is essential because they contribute to the overall work done on the object, thus ensuring the theorem's validity across different frames of reference, be they inertial or non-inertial.