What type of motion a rigid body may have when it is fixed along an axis?
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When in motion, a rigid body is believed to be a system of particles. Each of its particles follows a path depending on the kind of motion it follows. In a translational motion, all the particles move and behave in a similar manner. But in rotational motion, the rigid body dynamics indicate a different behaviour.
All the particles behave differently. Since rotation here is about a fixed axis, every particle constituting the rigid body behaves to be rotating around a fixed axis. As the distance from the axis increases the velocity of the particle increases.
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