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Consider an object say O (which is a rigid body having appreciable dimension wrt its orbit) is rotating about a fixed point C (and it is not spinning about its axis through centre of mass) at centre of circular orbit then

At first guess we would assume that the body is just translating and all particles at some instant have same velocity but if we analyse motion of particles more carefully we would find that each particle is moving in a circle about the axis through C hence it probably is doing both translation and rotation simaltaneously as different particles have different radius of orbit as body has appreciable size hence different velocities therefore not in pure translation.

So what kind of motion is this exactly?

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For motion of an ideal rigid body restricted on a plane, there exists an axis of rotation(called the instantaneous axis of rotation) about which the body is purely rotating with no translation. For any other axis, the body is translating as well as rotating about that axis.

In the case of unrestricted (general) motion I think the analog is that there exists an axis about which the motion can be described as rotation about that axis and displacement along that axis(In other words motion resembling a screw.)

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  • $\begingroup$ I am sorry I cant undersand what you're trying to say. What is motion resembling screw exactly ? What you're saying i true for say a wheel but how is it true for planetary orbital motion ? $\endgroup$ – Matt Apr 29 '17 at 10:05
  • $\begingroup$ The twisting motion that a screw does when you unscrew/screw something. The screw rotates about its symmetry axis and also displaces along it. $\endgroup$ – Abhijeet Melkani Apr 29 '17 at 10:06
  • $\begingroup$ But how is it related to the motion described in my question ? I explicitly stated that it is not moving about its axis through com. $\endgroup$ – Matt Apr 29 '17 at 10:07
  • $\begingroup$ Essentially, the "kind of motion" that a body executes depends on the axis chosen. You can always find an axis about which the body is purely rotating. That is all the particles in the body have velocity $v_i = \omega \times R_i$ about that axis. For some other axis it is rotating as well as translating. $v_i = \omega \times R_i + v_0$ (for a different $\omega$ and $R$) $\endgroup$ – Abhijeet Melkani Apr 29 '17 at 10:11
  • $\begingroup$ So you're saying if axis passes through C perpendicular to plane of motion then when body is moving in a circle it must always has to rotate About its symmetry axis ?? $\endgroup$ – Matt Apr 29 '17 at 10:13

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