Can a body be in pure rotation motion?

I am in high school and my textbook says that

"a body is said to be in pure rotation if every point on that body moves in a circular path about a fixed axis of rotation"

but my doubt is that at any moment, I can define a linear velocity as $$V=R\omega$$ for any particle of that body, where $$R$$ is the distance of the particle from the axis of rotation.

but as velocity is defined in straight line motion then how can we say that the object is rotating?

1 Answer

Notice, $$V=R\omega$$ is the linear or tangential velocity of any particle of a body rotating at angular speed $$\omega$$ at a particular instant of time $$t$$ because the tangential velocity $$V=R\omega$$ keeps on changing in direction from instant to instant while the magnitude $$R\omega$$ is constant if angular velocity $$\omega$$ of rotating body is constant.

Therefore, every point of a rotating body has a linear or tangential velocity at a every instant of time. A body moving at a velocity $$V$$ along a straight line can also be assumed to be moving on circle of ideally infinite radius.