Question

Is the work-energy theorem valid in a non-inertial frame?

Answer 1

Hint: In order to answer this question, we need to understand that the work-energy principle is valid even in the case of any non-conservative force. As we can see that we are making use of the work energy theorem for the work done by the resultant force, this theorem is valid everywhere. Hope these all may help you to solve this question.

Complete step by step solution:
As we all know that all objects in motion are having kinetic energy. Hence there will be a relation between the work done and the kinetic energy. This relationship between the kinetic energy of a body and the work done is known as the “Work-Energy Theorem”. It can be expressed in the form of equation,
$$W=\mathrm{\Delta }K$$
Here, W be the work done in joules (J) and $$\mathrm{\Delta }K$$ will be the change in kinetic energy of the body.
An accelerated frame is called a non-inertial frame, that is, in which the body is accelerating.
We can apply the work energy theorem in a non-inertial frame provided we take into account the work done by the pseudo force also.
Since the dynamics of a body cannot be explained in a non-inertial frame with real forces only so work-energy theorem is not valid but if we consider pseudo forces and Newton's laws can be applied and non-inertial frame can be treated as an inertial frame and work-energy theorem is valid.

Note:
It should be remembered that initially, the rule came from Newton's second law, and hence it is applicable to the particles. Objects that are like particles are considered for this rule. So, if all the object particles behave like particles, we can consider the whole object as a particle.