Why can Different Particles have Different Velocities when Rotating When a rigid object moves linearly, all particles within the object must have the same velocity or the object will split apart. However, when dealing with a rotating object, we know that tangential velocity is dependent on the distance of a particle from the center so different particles in the object can have different tangential velocities. What makes rotation inherently different from pure translational motion to allow this?
 A: For a body to remain rigid, the distances between particles must remain constant. That is, given any two particles p1 and p2, the distance between p1 and p2 must remain constant. This is known as an "isometric" transformation. For the distance to remain constant, the difference in their velocities must be perpendicular to the displacement between them; if the relative velocity had any component parallel to the displacement, then the magnitude of the displacement would be changing. If you have two particles with relative velocity perpendicular to the displacement, then you have rotation. If the relative velocity is zero, then you have translation. So what makes displacement different is that there isn't any rotation, and your question boils down to asking "What's different about rotation that allows rotation?" If there's rotation, then by definition, there's nonzero relative velocity. If there's no relative velocity, there's pure translation. Rotation is simply the state of having nonzero relative velocity. It doesn't "allow" nonzero velocity, it is defined by there being nonzero velocity.
A: You are worried about rotation causing the body to split apart because nearby atoms are moving at different velocities. Rotation does indeed cause stress in the material, and if it rotates fast enough it can break apart. For example, flywheels to store energy spin very fast and must be built of strong materials that can withstand the stresses. But at reasonable rotation speeds, the interatomic forces are strong enough to hold the object together.
