Solve & explain
Q).  Which of the following depends on the choice inertial reference frame?
(1) Momentum
(2) Change in momentum
(3) Kinetic energy
(4) Both (1) & (3)

Dear Student,


The right choice is option 4. i.e., both Momentum and Kinetic energy depend upon the frame of reference in which they are observed or measured.

Momentum is given by $\stackrel{\rightharpoonup }{P} = m\stackrel{\rightharpoonup }{v}$ here mass is a scalar and in whichever frame of reference an observer is the mass of a particular object does not change. But in the case of velocity reference frame plays an important role.

 For an observer standing by the road a passing by car wil have a considerable uniform velocity have a certain momentum but if the same car was observed by another person in another car moving with similar velocity the first car might not have any velocity at all (when we say velocity its uniform velocity  for a reference frame. Inertial frames are of rest or of uniform motion after all).    

The same can be said for Kinetic energy also after all Kinetic energy is also a dependent on velocity or more suitably on momentum.

K.E = 1/2 mv² = P²/2m


​Now as for why the change in momentum is independent of  the choice of inertial frame of reference. By definition we have   $F = \frac{dP}{dt}$ 
i.e., whenever there is a momentum change it implies that a force is acting on the system and as per the definition of an inertial frame all bodies in the frame will continue in its state of rest or of uniform motion unless an unbalanced external force acts upon it.

In inertial frames bodies can have acceleration and that acceleration will be proportional to the applied force.  Now the body that has been accelerated will continue in that state unless another force acts upon it. Even from observing from different frame of reference the acceleration produced on a body due to an applied force will not change.

Consider a batsmen hitting a ball or kicking of a football. Wherever the observer ( whichever inertial frame) is they will all see that the ball changed its velocity or accelerated according to the force imparted by the bat or leg of the player. Thus the force or the change in momentum with time is independent of choice of  inertial frame of reference.




I hope the given explanation is clear enough for you.




regards
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