Problem in choosing axis in rotational mechanics?

AI Thread Summary
Choosing the correct axis of rotation in rotational mechanics can be confusing, particularly in problems involving rods and forces. In the first example, the angular velocity of a rod after it recoils depends on the axis chosen, with the instantaneous axis of rotation being crucial for accurate calculations. For the second scenario, it's suggested to take the axis around the point where the rod touches the surface, using the moment of inertia and torque to find angular acceleration. However, if the center of mass is used as the axis, the resulting answers differ due to the need to account for additional torques, such as those from the normal force. Understanding the implications of the chosen axis is essential for solving these types of problems effectively.
vkash
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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.
 
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angular velocity is a vector, and it doesn't matter what axis you chose, it will be the same.
 
Curl said:
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.
 
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.
 

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