# Kinetic energy of rigid body

1. Feb 6, 2010

### zhenyazh

hi,
when will i use 0.5mv^2 and when will i use 0.5Iw^2
when will i use both?
as far as i can see one represents the movement of the center of mass and the other
the angular movement.
so as far as i understand for a moving cylinder i would use the sum of those.
but i can't think of any example where i use only one.
for instance what happens in the following cases:
1. circular motion of some ring
2. a rod which is fixed to the wall on one side is being hit on the other and starts rising
3. a rod that lies on a table, gets hit by clay and starts moving. this one is not fixed.

thanks a lot
this forum is really helpful in preparing for my exam

2. Feb 6, 2010

### Staff: Mentor

If you take I about the center of mass, then you can always use both. One represents the KE due to the translation of the center of mass; the other is the KE due to rotation about the center of mass.

But sometimes you can treat a body as being purely in rotation about some axis and just use KE = 0.5Iw^2, where I is about the axis of rotation.

I don't understand this case.
Since the rod is hinged at one end, you can treat its motion as being pure rotation about that end.
Use both, with I about the center of mass.