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Planar motion:A rigid body B is said to be in planar motion if each particle of B moves in a fixed plane and all these planes are parallel to each other.

This is my understanding of this definition. If a motion of rigid body has 2D motion then It is said to be planar. I think including the idea of plane is unnecessary but I am sure I kinda didn't get the definition properly. So please help!

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  • $\begingroup$ There are so many links in the web ??? Did you try to find them ??? $\endgroup$
    – Frobenius
    Commented Apr 30, 2020 at 9:40
  • $\begingroup$ @Frobenius I googled it and most of them makes sense but not complete sense to me. I watched video and very few of them have it and none provides intution to me. $\endgroup$
    – banned
    Commented Apr 30, 2020 at 9:42
  • $\begingroup$ I don't think that planar motion is 2D motion. Suppose the axis of Earth is normal to the plane of its elliptic orbit. Then every Earth point is moving parallel to that plane, that is we have planar motion. But this motion is 3D (translational+rotation around Sun+rotation around Earth axis). $\endgroup$
    – Frobenius
    Commented Apr 30, 2020 at 9:56

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Your intuitive understanding seems reasonable, but it is not rigorous enough to be considered a definition. After all, it would be strange if you could define planar motion without resorting to the concept of the plane.

Indeed, when you define planar motion in terms of "2D motion", you failed to define what "2D motion" is. Can we allow it to be a motion constrained on any 2D surface? If so, this would include motion on a sphere or a torus, which is definitely not planar motion. So it must be more restricted than this. In this context you can either say: "2D motion is planar motion", which is circular reasoning, or "2D motion is motion constrained on a plane", which is where the concept of the plane was hiding all along.

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  • $\begingroup$ To ensure that the motion is rigid, i.e. that the distance between particles is kept constant and the body does not deform. But now that you mention it, the definition is not strict enough. It rules out deformation perpendicular to the planar motion, but it does not rule out stretching along the plane. A more rigorous definition should not only require that the displacements of the particles are restricted on parallel planes but also that all the particles are equally displaced. $\endgroup$
    – zap
    Commented May 2, 2020 at 11:09
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In the "Arya" and "Simon" classical mechanics,we explain the rigid body as some particles often in case of Avogadro number and distance of between each 2 particles is fixed and based on Newton third law of motion,force between particles will be zero.we do not have any ideal rigid body in nature that always above conditions are true but most of the time, with some Approximation,we say that they are rigid body.another point about rigid bodies is that they have a point called "center of mass" that we can imagine all the mass of the object is in the center of mass and we can re-write the laws of the motion for the point instead of whole rigid body. hope to be useful but it is better to take a look to the classical mechanics references.

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A rigid body B is said to be in planar motion if each particle of B moves in a fixed plane and all these planes are parallel to each other.

Where did you pick up this definition? In my opinion, planar motion of a rigid body means that only the center of gravity of the body is moving in a fixed plane but not necessarily all of it's particles.

According to the definition you posted, a rotating body cannot be in planar motion (except the rotation is around an axis perpendicular to the plane of motion).

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