A body is in pure rotation, The linear speed υ of a particle, the distance r of the particle from the axis and the angular velocity ω of the body are related as Thus

Question

Philoid · Accepted Answer

eq.1

There are two arcs DE and NC. They are at different radii. Both of them swipe the same angle θ. Let us calculate the angular velocity.

Linear velocity(DE)

Form eq.1,

Linear velocity(NC)

Form eq.1,

So, we can see that

Hence, ω is independent of R.