Question

Why is the Kinetic Energy least in COM frame out of all the possible frames ?

Answer 1

@ProfBrainstorm , could you please help me ?

Answer 2

There is a general result in mechanics, that the total kinetic energy of a system, in an arbitrary frame of reference, can be expressed as the sum of the kinetic energy of the parts of the system as seen in the centre of mass frame, plus the kinetic energy of the motion of the centre of mass as seen in the arbitrary frame.
Now if we happen to choose the centre of mass frame as our frame of reference, then the centre of mass is of course stationary, so we have eliminated that contribution to the kinetic energy, hence the kinetic energy is a minimum in the centre of mass frame.

Answer 3

But , the overall sum of terms in other frame can still be less than than that of COM frame . I mean , no guarantee right ?

Answer 4

Even though that term is zero , still.

Answer 5

i don't follow your question

Answer 6

if you compute the kinetic energy of a system in various frames of reference, you will find that the kinetic energy is least when viewed in the centre of mass frame, guaranteed

Answer 7

Since , KE changes with frame of refrence , how can we be sure that the (sum KE of sys,com+ KE com , ground) will be less than ( KE , in com frame +0 ).

Answer 8

Yes , I did see that in a few questions !

Answer 9

I still don't quite see your problem
Let us suppose that we calculate the KE of the system in the centre of mass frame, and call it E1.
If we now calculate the KE in some other frame of reference where the centre of mass is moving with speed V, then we will find that the kinetic energy is now equal to E1 plus 1/2 MV^2 where M is the total mass of the system.
Clearly then, the total kinetic energy in an arbitrary frame will always be larger than E1, because 1/2 MV^2 is always positive.

Answer 10

Hope that has helped.

Answer 11

yes , it did . Thanks a ton !