Will a free falling rod rotate or not?

Main Question or Discussion Point

Will a free falling rod rotate ?

When we consider a bicycle is turning on a flat plane, we know that there is friction, which provide centripetal force on the bicycle. And we know that the bicycle is no longer perpendicular to the flat plane so as to reach equilibrium. What I want to ask why we always choose the center of gravity of the bicycle be the rotational center. Just like when a rod is free falling and parallel to the ground, if I choose the center of gravity as the rotational center the rod will not rotate, because there is no net moment acting on the rod. But if I choose the points other than the center of gravity as the rotational center, there would be net moment due to gravity and the rod will rotate. Will the rod rotate or not? Why we always choose center of gravity as the rotational center?

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Answers and Replies

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And we know that the bicycle is no longer perpendicular to the flat plane so as to reach equilibrium.
So no one rides a bike upright?

But if I choose the points other than the center of gravity as the rotational center, there would be net moment due to gravity and the rod will rotate. Will the rod rotate or not? Why we always choose center of gravity as the rotational center?
We choose the center of gravity for simplicity. If you use another point in the body for the center of rotation, you have to use the parallel axis theorem.

But when I choose the other point as rotational centre and chage the moment of inertia by parallel axis therom, there are probabilities for the rod to rotate or not.

if I choose the center of gravity as the rotational center the rod will not rotate, because there is no net moment acting on the rod.
Ok
But if I choose the points other than the center of gravity as the rotational center, there would be net moment due to gravity and the rod will rotate.
There would NOT be net moment.
Imagine a massless rod AB. On the extreme B of the rod let's put a weight.
Let's put the rod horizontal and let it fall.
As said before, if I choose B as center of rotation, the rod will not rotate.
If I choose A, the forces acting of B will be $mg$ pointing downwards, and $ma$ pointing upwards. Of course $a=g$
That's because the body is accelerating, and with accelerating bodies you should always consider the fictious force $ma$.
Again, no net torque.
Will the rod rotate or not?
Of course not. The result must be the same regardless the method you use to study it.
Why we always choose center of gravity as the rotational center?
As you see, you can choose any point you like.

Thank you very much .In the case of bicycles, how should I consider the net moment acting on the bicycle if I choose the point where the friction and the normal reaction acting on.