Problem in choosing axis in rotational mechanics?

[vkash]

In rotational mechanics i am mostly confused with the axis of rotation. Let me give you some examples of question.

A rod of length l falls on two pads of same height from height h(rod is initially horizontal to plane when it is at height h). The coefficient of restitution of the metal pads are e₁ and e₂(e₁ > e₂). The angular velocity of the rod after it recoils is__________

about which axis. Is that instantaneous axis of rotation.
OK this may seem to be solved here but what about this question.

A uniform rod of mass length l is held stationary in vertical position on a smooth horizontal surface.Find angular acceleration of the rod in this position when horizontal force F=mg is applied at it's topmost point.

Now once again. which axis should i choose.
IAOR(instantaneous axis of rotation). I can;t find that.
However when i see solution of this example they take torque around the center of the rod and solve it. Why they take center of the rod. Why not any other point. If any other point on the plane is taken then answer may vary.
this point is really confusing me in rotational dynamics. which axis should i choose when i do questions.

please help me.!

I think general physics is correct place for this question.

 

[Curl]

angular velocity is a vector, and it doesn't matter what axis you chose, it will be the same.

 

[vkash]

angular velocity is a vector, and it doesn't matter what axis you chose, it will be the same.

In second question, Take axis around point where rod touches the surface.
$$I=\frac{ml^2}{3}$$
$$T(Torque)=mgl$$

$$T=I\alpha$$
$$\alpha=\frac{T}{I}$$
$$\alpha=\frac{mgl}{\frac{ml^2}{3}}$$
$$\alpha=\frac{3g}{l}$$
Now take the center as the axis. Your answer will $$\frac{6g}{l}$$. That's different.
How will you explain this with our answer.

 

[Curl]

If you take torques about the CM, then you must also account for the torque by the ground (the normal force).

If you sum torques about the ground, make sure you compute the inertia about the end of the rod. Use the parallel axis theorem.

 

[PJC01]

I can understand your confusion and frustration with choosing the axis in rotational mechanics. It is a common problem that many students face when learning about rotational dynamics. The key to understanding this concept is to remember that the axis of rotation is an imaginary line around which an object rotates, and it is always perpendicular to the plane of rotation.

In the first example you provided, the axis of rotation would be the line passing through the center of the rod. This is because the rod is falling in a vertical plane and the rotation is occurring around a fixed point. The instantaneous axis of rotation would be the same as the axis of rotation in this case.

In the second example, the axis of rotation would still be the line passing through the center of the rod, but the rotation is not occurring around a fixed point. Instead, the rod is rotating around its center of mass due to the applied force. The torque is calculated around the center of the rod because it is the point where the force is applied, and it is the point that experiences the greatest change in angular velocity.

It is important to note that the choice of axis of rotation is arbitrary and can vary depending on the problem. However, choosing the center of mass as the axis of rotation is often the simplest and most convenient option. In more complex problems, you may need to choose a different axis of rotation.

In conclusion, the key to choosing the correct axis in rotational mechanics is to understand the motion of the object and the point around which it is rotating. Once you have identified these, you can choose the appropriate axis of rotation to solve the problem. I hope this explanation helps to clear up any confusion you may have had.