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Homework Statement
This is a very simple problem to state, yet I've not found any answers on PF or anywhere else online.
So let's say we have a simple rigid body like a rod. We apply an external force Fext for a fixed time dt to the rod in two different ways: (1) directly on the center of mass and (2) on the side of the rod. In both cases, we have the same motion of the center of mass, and hence the same kinetic energy associated with the center of mass. However, in (1) the rod does not rotate, whereas in (2) it does as we've applied a torque relative to the CM. So in (2) we have an extra kinetic energy of rotation in addition to the kinetic energy for the CM's motion. How is this possible, given that we applied the same force for the same time in the two instances? Doesn't this violate the fact that we did the same amount of work "input" in the two cases?
Homework Equations
Fext= MACM
T =0.5mv2
The Attempt at a Solution
N/AThanks for all the help.