# How to explain centrifugal force from frame of reference of Earth?

Suppose we have a circular table. We have made a straight line groove in the table extending from the center to the circumference. Now we place a block at some distance from the center in the groove and start rotating the table. Suppose there is no friction between the walls of groove and the block.

Result: The block finally moves out of the groove.

If we consider the rotating frame of reference of the table, this motion can be easily explained with the help of centrifugal force which acts radially outward on the block.

But when we consider the frame of reference of earth, I was not able to explain it. There are no radially outward forces on the block, just the normal reaction from the walls of the groove(which acts in a direction perpendicular to the groove) and the weight of the block(which acts downward).

So how does the block eventually move out of the groove?

• Wrong question! Should be: why does the table move out from underneath the block...? – DJohnM Sep 21 '14 at 13:56
• I did have a similar question and i sill didn't receive an answer: physics.stackexchange.com/q/332959 – Physicpsycho May 29 '17 at 15:29

If you sit in a driving car that turns, you feel squeezed to the side. You are moving straight ahead, and suddenly the car changes direction. So it tries to take you along. It if not you who squeezes against the side, but rather the car that squeezes into you.

This tendency to keep moving straight ahead is what causes the feeling of the centrifugal effect. When the car turns, your body still wants to keep going straight out. On the rotating table, the block wants to move straight out, and does so by sliding along the groove. The sideways normal forces make it change directions but don't prevent motion along the groove.

What is explained by pseudo force in a non-inertial frame can mostly be explained by inertia from an inertial frame. Let see an example: 1. Linear motion- Suppose that the floor of a coach,moving with uniform speed in a straight line,is frictionless. A passenger inside the coach rolls a ball on this floor along the direction $AB$ which is perpendicular to the direction of motion of coach. It will be seen that the ball follows the line $AB$, irrespective of velocity of the coach as long as it remains constant. No deflection will be observed from the ball's initial direction of motion,although the coach has moved through a certain distance during the interval of time taken by the ball. For an observer,fixed on ground,this is an example of inertia of motion. He will say the ball is not deflected from the line $AB$ as it retains its forward velocity which is equal to the velocity of the coch,due to its inertia of motion. Now,let us assume that the train is moving with a uniform acceleration,$f$ . If the passenger pushes the ball along the ball along the direction $AB$, the ball will not move along $AB$ ,but will be deflected backward and will move along a curved parabolic line,say $AC$ . This happens,from the perspective of passenger,because there is a force $m.f$ ($m$ being the mass of the ball) acting in the opposite direction of motion of the train and that is pseudo force. But from an observer from the ground ,this occurs because of the fact that the point $B$ moves a distance $CB$ ahead of the ball during the time in which it comes from one side of the coach to the other. When the ball is let go from $A$ ,its forward velocity remains unaltered due to inertia of motion but the velocity of the coach increases continuously with time,causing the ball to fall behind the line $AB$ (the ball will lag behind continuously at the same rate w.r.t to the passenger) . And hence the ball deflects which the observer in the coach sees as the ball moving with acceleration $-f$ . Thus it is inertia which plays the role with respect to an inertial frame. Now , coming to the circular motion, let us give an example: 2. Suppose,we are inside a train that is moving at uniform speed & that the train is leaving the straight portion and entering the curved portion. If the passengers are unaware of the fact that the train is going in a circular track,they might explain their motion as being due to some horizontal force. Let us suppose that a ball had been placed on the floor of the train while it was moving with uniform speed in a straight line. The ball would remain at rest on the floor until the train starts going around the curve. It would then roll towards the side of the train further removed from the centre of the circular path. A passenger inside the train might ascribe this motion to the action of a "centrifugal force" on the ball. To the observer in the stationary frame of reference ie. outside the train - the ball would simply be moving in the same straight line along which it had been moving during the time that the train was moving along the straight portion of the track. This follows from Newton's first law of motion because there is no unbalanced force acting on the ball. Thus,what had happened due to centrifugal force in a rotating frame was simply due to inertia from a stationary frame of reference. Now you can think your own example . In a nutshell, inertia is what your answer is.