Will an object resting on a rotating platform move in a frictionless world? Imagine that a pebble is placed on a uniformly rotating, frictionless disk.  What will happen to this pebble? Will the disk slide under it and the pebble stay as is? Or will there be a centrifugal force on the pebble and it'll be thrown off the disk?
 A: Let's assume that this whole setup is being viewed from an inertial frame and that if there is gravity, then it points perpendicular to the plane of the disk, then
The disk will slide under the pebble, and the pebble will stay where it is.
Why?  Well in an inertial frame, Newton's second law holds.  Since the force on the pebble tangent to the surface of the disk is zero when there is no friction, the acceleration of the pebble will be zero.  Therefore, it's velocity will be constant, and if it's velocity started at zero, then it would remain zero for all later times.
A: In that case the pebble won't move. 
If there is no friction, there won't be any forces between the pebble and the disk.
A: Pebble will not move according to a inertial frame outside the disk which is rest with respect to ground,Since looking from this inertial frame,there is no horizontal force acting on pebble because of frictionless.Hence accoring to newton's $2^{nd}$ law pebble will stay in its state according to a observer from ground.
But for an observer rotating along disk$($non-inertial frame,we have to include pseudo force$)$  see that pebble is under centrifugal force acting on it and for his observation the pebble will move relative with him and dynamics given by newton $2^{nd}$ law,ie $ma=centrifugal force$
