# Spring rotated in uniform circular motion

Why does a spring stretch when rotated in uniform circular motion? The horizontal rod containing the massless spring(stiffness = k) and block of mass 'm' is rotated uniformly about point P. This centripetal force is provided by the elastic(restoring) force of the stretched spring which is 'kx' where x is elongation of the spring as compared to rest position.

Everything looks very neat very decent.

I am listing the problem as seen from two reference frames.

## 1. Rotating frame (as seen from rod).

As seen from the rod, centrifugal force is acting outwards. This will cause the block to move towards right, and hence stretching the spring. The centrifugal force will be balanced by the spring force acting left. Everything seems fine.

## 2. Inertial Frame (ground)

I am unable to understand why does the spring stretch in the first place? There is no reason why the spring should stretch. Their is no force acting on the block in the outward direction. There is a centripetal force acting on the block when it is undergoing rotation. But that force is towards the center. So the spring should contract???

## 1 Answer

For the block to move in a circle, there must be a centripetal force (as you have said)--something needs to be constantly pulling the block toward the center of the circle if it is to move in a circle. The thing that does the pulling in this case is the spring. (In other words, the source of the centripetal force is the spring. Without the spring, there is no centripetal force, assuming there is no friction between the block and the rod.)

If this is not clear, imagine what would happen if the spring was not attached to the block. When the rod begins to rotate, the block will soon slide off the end of the rod because we know from Newton's First Law that the block will try to move in a straight line unless we apply a force to change its direction. If the spring is attached to the block, however, when the block tries to go straight and slide off the end of the rod, the spring will stretch and apply a force toward the center of the circle. That will prevent the block from flying off the end of the rod.