# Rotation of non-rigid bodies-centrifugal effect

Suppose that we have a bar of finite length which is rotating about its center of mass at a constant angular velocity in a horizontal plane. Gravity is neglected.

The fact that the bar stretches outwards is supposedly explained by the centrifugal effect i.e. the presence of a centrifugal force which acts radially (outwards) on the bar's constituent particles. However what concerns me is the fact that this force is only supposed to be present in a rotating reference frame, which suggests that if I observe a rotating bar in an inertial frame, I should not witness any elongation at all, which is obviously false. So if I am in an inertial frame, how am I supposed to explain the elongation of the bar?

## 2 Answers

According to Newton first law, the edge of the bar prefers to continue in a straight line (tangential). It is being pulled inwards (radial) by the centripetal force to keep the circular route. Hence the elongation.

The only difference you will observe from an inertial frame is that the centre of mass of the rod will gain some velocity with magnitude equal to the velocity of the inertial frame.

Angular velocity of the rod will suffer no change due to this.

A rod which is both translating and rotating can be considered as a superposition of pure translation and pure rotation.

The rod elongates due to the centrifugal force which is a consequence of a definite trajectory (a circle) of infinitesimal segments that make up the rod. Magnitude of this force is independent of the frame of observation because angular velocity of the rod for all such frames in equal. Velocity of centre of mass will have no contribution to the elongation of the rod under observation.