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## Homework Statement

This problem is taken from Kleppner's

*Intoduction to Mechanics*and is problem 2.29.

A car is driven on a large revolving platform which rotates with constant angular speed [itex]\omega[/itex]. At time [itex]t=0[/itex] a driver leaves the origin and follows a line painted radially outward on the platform with constant speed [itex]v_0[/itex]. The total weight of the car is [itex]W[/itex], and the coefficient of friction between the car and stage is [itex]\mu[/itex].

a. Find the acceleration of the car as a function of time using polar coordinates.

b. Find the time at which the car starts to skid.

## Homework Equations

Acceleration in polar coordinates [itex](\dot{r}\ -r \dot{\theta}^2 )\hat{r} +(r \ddot{\theta} +2\dot{r}\dot{\theta})\hat{\theta}[/itex].

[itex] f_{MAX} =\mu W[/itex], where [itex] f [/itex] is friction.

## The Attempt at a Solution

So the acceleration is [itex](-v_0t\omega^2 )\hat{r} +(2v_0\omega)\hat{\theta}[/itex].

I think the time the car begins to skid when the frictional force cannot provide the necessary acceleration, or when the acceleration is [itex] \geq \mu g[/itex]. I would then find the absolute value of the acceleration, equate it to [itex]\mu g[/itex], and solve for [itex]t[/itex]. I'm not sure if this is correct, however.