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# Physics/Rotational mechanics

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Question
Are the angular displacement, velocity and acceleration described only for circular rotations? can we calculate these variables for a straight line path or say an ellipse? We can theoretically take torque of a force about any point or same for angular momentum, then irrespective of the point about which we take these quantities, will the motion be percieved in the same way.? for example, there are 2 forces acting on a rod placed somewhere in xy plane, if we only take the torques of the force about a distant point say origi, can we describe the motion with equal accuracy as when we take them about its axis of rotation or COM? the same holds for angular momentum. if possible, give an example which might help.

Answer
> only for circular rotations?

No, but circular motion is the main usage. Doing so for other motions complicates things AND gives less useful information.

> can we calculate these variables for a straight line path or say an ellipse?

Yes. Elliptical motion, in particular, exhibits conservation of angular momentum as well as circular motion.
http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html
Note that, for straight line motion, it's easier to use simple linear momentum. You'll get the same results as when you calculate for angular momentum, with a lot less mathematics.

> We can theoretically take torque of a force about any point
> will the motion be percieved in the same way?

You can measure angular momentum around any point you wish, but it's MUCH easier to do so when your point is within the axis of rotation.

This is all I wish to say on this topic.

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