# Kinetic energy of rigid body

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

Doc Al
Mentor
hi,
when will i use 0.5mv^2 and when will i use 0.5Iw^2
when will i use both?
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.

for instance what happens in the following cases:
1. circular motion of some ring
I don't understand this case.
2. a rod which is fixed to the wall on one side is being hit on the other and starts rising
Since the rod is hinged at one end, you can treat its motion as being pure rotation about that end.
3. a rod that lies on a table, gets hit by clay and starts moving. this one is not fixed.
Use both, with I about the center of mass.