# Force and Torque Question on an isolated system

If there's a rigid rod in space, and you give some external force perpendicular to the rod at one of the ends for a short time, what happens?

Specifically: What dependence does the moment of inertia have? If it rotates, what is the center of rotation? Does it matter that the rod is rigid? What happens if it's "springy", say a rubber rod instead. Is there a difference between exerting a force for a short period of time, and having an inelastic collision (say a ball hits the end of the rod instead of you pressing).

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– chase lambert Jan 15 at 11:21
What is the center of rotation though? – chase lambert Jan 15 at 14:15

## 1 Answer

The moment of inertia of a rod with a perpendicular axis of rotation through the center of mass is $$I=\frac{1}{12}ml^2$$ where m is the mass and l the length.

If you apply a torque $$\tau=r\times F$$ (all vectors), then $$\tau=I\alpha$$ lets you calculate the angular acceleration alpha.

If the rod deforms, energy will be needed for deformation and creation of heat. If the force F is exerted for a longer time, the total work on the rod has to be integrated over time. No. F has to be integrated to get the work.

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