Axis of Rotation: Rotate About Other Axes?

[aniket7tomar]

Does a body rotating about an axis also rotate about any other axis?
Eg. Cars on a racetrack may be rotating about a vertical axis passing through the centre of the track but can they also be considered to be rotating about a vertical axis passing through the spectators' stand?

 

[mathman]

Specific question - no. In general the terms rotate and revolve have different meanings. The Earth rotates about the axis defined by the north and south poles. The Earth revolves around the sun.

 

[aniket7tomar]

I think you misunderstood the question or i am unable to understand the reply...
What i asked was that in the fig. If body b is rotating about axis aa' then can we say that there can be an axis mm' parallel to aa' about which the body's motion can be described as rotation?
Can that happen with any axis parallel to aa'?

 

[UltrafastPED]

The moment of inertia will be different if you change the axis of rotation.

But while a moving body will have angular momentum wrt any stationary line, it will only have one instantaneous axis of rotation - this is the axis for which every element of the body has the same angular acceleration.

 

[Philip Wood]

I was going to say that if a rigid body is rotating about an axis, then each point on the body remains the same distance from the axis. Surely this can be the case only with a single axis.

 

[aniket7tomar]

I was under the impression that i understood your answer but then later i thought about how when a disc is rolling 'purely' we can consider it to be rotating about an instantaneous axis passing through the pt. in contact with the ground as well as a moving instantaneous axis through the centre of mass?
Pls. tell

 

[Philip Wood]

a7t: I see what you mean. My post exemplifies fools rushing in where angels fear to tread. I'd say that the instantaneous rotation axis was the line of contact with the ground, but it is certainly true that the velocity of each point on the disc can be constructed by adding a constant 'forward' velocity to a velocity due to rotation about a stationary axis through the centre of the disc. Nonetheless, in our ordinary frame of reference, I'd say it was not correct to claim that the disc is rotating about its centre. I suspect this is controversial. Let's hope you get more replies to your interesting question.

 

[D H]

I think you misunderstood the question or i am unable to understand the reply...
What i asked was that in the fig. If body b is rotating about axis aa' then can we say that there can be an axis mm' parallel to aa' about which the body's motion can be described as rotation?

Yes.

You can pick any arbitrary point on (or even off of) the body and describe the 6 DOF motion of the body as a combination of translational motion of that selected point plus rotational motion about an axis that passes through that point.

 

[D H]

A couple of specific examples:

1. A lever rotating about a pivot point, or a door that opens on a hinge. Here there is a fixed point (or set of fixed points) on the rotating object that doesn't undergo translation. It oftentimes make more sense to describe the behavior in terms of pure rotation about this fixed point than describing it in terms of translation of the center of mass and rotation about the center of mass. If you do the latter, you need to add constraint forces / constraint torques to the description so as to keep the fixed point fixed.

2. A rocket that goes from a vertical orientation on the ground to a horizontal orientation ten minutes later, in the process expelling 95% of its mass. With a center of mass description, you need to account for the fact that the center of mass moves within the rocket if you want to accurately model where that rocket will be after that ten minutes. There are different uglinesses that come into play a fixed point description (e.g., translation of / rotation about the nose of the rocket).