An everyday is example would be cars. If you were to drop a car, not taking air resistance into account, would a front-heavy car tumble forward as it fell? And a car with a perfect 50/50 front/rear weight distribution fall straight? Does mass distribution/center of mass affect free fall? Or would they both fall straight down without tumbling? Can you explain why please?
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If there is no resistance then there will be no net torque applied about the center of mass. So any initial rotational speed will remain. The rotation center is going to be the center of mass.
The effect of gravity will be to accelerate the center of mass, and it will have no effect on the rotational motion of the body.
See this accepted answer for a related question for the mathematical answer to your question. Here is what you need to take from this:
The rules of motion lead us the following equivalent statments that are valid for both 2D and 3D bodies:
- A pure force thorugh the center of gravity (with no net torque) will purely translate a rigid body (any point on the body).
- A pure torque any point on the body (with no net force) will purely rotate a rigid body about its center of gravity
John Alexiou
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