# How to find pseudo-force on a body in a non-inertial reference frame with respect to another non-inertial reference frame?

If there is a body in a non-inertial reference frame (say accelerating with acceleration $$A_1$$) and an observer in another non-inertial reference frame (say accelerating with acceleration $$A_2$$) what would be the pseudo-force acting on the body (say it has mass $$m$$) as seen by the observer? Both $$A_1$$ and $$A_2$$ are in the same direction and along a straight line.

Do I simply need to find the relative acceleration of the first frame with respect to the second frame and multiply the relative acceleration with the mass of the body?

• I'm not sure if I understand your question but The inertial force a body feels from acceleration is independent of what other bodies are doing. – Bill Alsept Sep 21 '16 at 0:01
• Okay, that means it doesn't depend on what an observer sees. Is it true for all kinds of forces acting on a body? i.e. independent of what an observer sees from another reference frame? – Debarun Mukherjee Sep 21 '16 at 3:45

The pseudo force depends only on the acceleration of the observer frame (which is why if the acceleration of the observer is zero (in the inertial reference frame case) there is no pseudo force.)
Therefore, given that the acceleration of the observer is $$A_2$$ the pseudo force acting on any body (which has mass $$m$$) observed will be $$-m \cdot A_2$$.
No, we do not take the relative acceleration of the observer and the body observed but the acceleration of the observer as measured by any inertial frame.