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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).

Waffle's Crazy Peanut
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chase lambert
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2 Answers2

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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.

Metalbeard
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The moment of inertia is the rotational mass of the object and it is solely a function of mass distribution - the shape. Usually it does not matter if it is rotating, but if the rate of rotation is high enough the body could deform. This is a concern in the connecting rods of high speed engines.

The MI does depend on shape, so it will change if the material is not rigid. However, angular momentum will preserved so the object will rotate faster when the MI is smaller.

The center of mass does not change unless acted on by an external force. But that force is being applied from another mass, so an "external" force does not really exist.

Inelastic collisions should be analyzed using the conservation of momentum, and not energy. Then it does not matter the duration of the force, or the strength, just the integrated amount.

Energy is also conserved in the collision, but in an inelastic collision energy is transformed into heat preserving the conservation rule, while providing no help for our solution.