# Q & A: Kinetic energy of moving and rotating objects

Q:
A thin hollow sphere of mass m is completely filled with a liquid of mass m . When the sphere rolls with a velocity v , the kinetic energy of the system will be? (neglect friction)
- ARVIND (age 38)
MODINAGAR, UP, INDIA
A:
There are two components of the kinetic energy in this problem.   The translational motion which both the hollow sphere and liquid contribute to and the rotational part which only the hollow sphere contributes since the liquid is presumably not rotating..   The former is 1/2 mv2 for both.  The latter is 1/2 Iω2 for the sphere.  Here, I, is the moment of inertia of the sphere and ω is the angular rotation speed, v/r.

LeeH

p.s. Thanks to viscosity in the liquid, it will gradually start to rotate along with the the hollow shell. So the answer depends on if you catch the process early, as Lee described, or late, when there's just one rotation rate. Maybe when they say "no friction" they mean neglect viscosity, so it's always like Lee described. /Mike W.

(published on 08/18/2011)