# What is the physical explanation for the fact that particles at the axis of rotation during rotational motion do not rotate?

During pure rotational motion, the particles at the axis of rotation are said to be not rotating, doing maths on it we get proof as well.

v=linear velocity, ω=angular velocity and r=distance of the particle from the axis of rotation,

v=ωr ⇒ v/r=ω

for the particles lying at the axis of rotation, v=0, and r=0, so the ω becomes indeterminate.

but physically observing a rotating body(like a wheel), even the particles at the axis of rotation seem to be rotating. Help me understand it by mentioning physical explanation for this.

• The point at the center does not move, its spatial position does not change with time. It might be hard to imagine because when you look at it you always see a finite patch, not a single point. Just imagine how fast points close to r move, the smaller the r the smaller their speed.
– user126422
Commented Apr 15, 2017 at 3:49
• To re-express what @ArmandoEstebanQuito says: the points on the axis don't translate, but they do rotate. There rotation may be uninteresting if they exhibit the correct symmetry, but if they are contributing to, say, an off-axis magnetic moment then that moment turns. Commented Apr 15, 2017 at 4:06
• Commented Apr 15, 2017 at 4:19

The particles at the axis do rotate. They do not orbit around the axis, because the axis passes through them, but they still rotate or rather spin with the same angular velocity $\omega$ as the other particles in the object.
The fact that mathematically the angular velocity is indeterminate at the axis does not mean that physically it is zero or is any different from the rest of the object. In the limit $r \to 0$ the ratio $\frac{v}{r} \to \omega.$