# How will “a block on a turntable” move when the turntable move very fast?

If there is a block that is placed at the rim of a turntable, and we start rotating this turntable, I know that while the turntable is rotating, a centripetal force is acting on the block. This force is static friction. If we increase the angular speed of the turntable, the static friction must increase (according to newton's 2nd law with the normal direction $F=mv^2/r$, where $v$ is the speed of the block, $r$ is the radius, and $m$ is the mass of the block). If we continue increasing the angular speed of the turntable, kinetic friction will act as a centripetal force instead of the static friction and the block will slip. My question is, in what direction will the block slip? Will the block slip in the tangential direction? Or will it slip at an angle from the tangential direction?

My expectations(I don't know if this is true) is that according to newton's 2nd law $F=mv^2/r$, since $v$ is very large and $F$ (kinetic friction force) is very small, then $r$ must become very large. When the radius of any circle (in general) is very large, the circle becomes like a straight line (I mean that a straight line is a circle such that the radius goes to infinity, so as $r$ gets larger, the block will kinda move in a straight line), which means that the block will slip in the tangential direction.

• Which reference frame are you in? From the reference frame of the turntable, the block will slip away from the center. From the reference frame of someone standing on the "sidelines" and observing the block, the path of the block will be somewhat more complex, and will depend on the coefficient of kinetic friction and the angular acceleration of the turntable. – David White Jun 27 '17 at 15:45
• @Eman.suradi : Thanks for your comments to my answer. Sorry I am confused myself. What I should say is that the static limit applies in the direction of attempted motion. I am deleting my answer temporarily and shall revise it within a couple of days. – sammy gerbil Jun 28 '17 at 14:25
• @sammygerbil I am waiting :) – Eman.suradi Jun 28 '17 at 15:14
• @sammygerbil .. – Eman.suradi Jul 8 '17 at 20:24

• Yes, I mean that using comoving polar coordinates $(r, \theta)$ you see that "straight line" (fixed-reference-frame) trajectory appear to go towards increasing $r$ in a sort of parabolic way, and then, due to the Coriolis force, decreasing $\theta.$ As sammygerbil says in the other answer, this is all based on assuming very low tangential accelerations so that what "gives" is that the centrifugal force exceeds the static friction force limit. – CR Drost Jun 28 '17 at 14:13