How Far Can the Block Be Placed on a Rotating Turntable Without Sliding Off?

[siralan]

The coefficient of friction between a certain brass block and a large revolving turntable is µ = 0.26. How far from the axis of rotation can the block be placed before it slides off the turntable if it is rotating at 33 1/3 rev/min?

 

[Doc Al]

Consider that it is friction that supplies the centripetal force.

 

[gerben]

As long as the force that is needed to overcome friction is larger than the centripetal force the block will not move.

$$F_{friction} = F_z \mu = mg\mu$$
$$F_{centripetal} = \frac{mv^2}{r}$$

so you can move the block from the axis of rotation until these are equal, and when they are equal this holds:
$$mg\mu = \frac{mv^2}{r} \Leftrightarrow g\mu = \frac{v^2}{r}$$
and using $v = r*v_{rotational}$ you can solve this