Static friction and centripetal force

[Xamien]

Homework Statement

"If the coefficient of static friction between the block of mass m and the turntable is $\mu_s$, determine the maximum constant angular velocity of the platform without causing the block to slip." I'm actually using this problem to understand why I'm getting the wrong answer to another question, unfortunately the book doesn't actually say if I have the right answer to THIS one. r is the radius, of course.

Homework Equations

$f = \mu_s F_{n}\ F = m r \omega^2 \ \sum F = F_1 + F_2 F_{n} = m g$

The Attempt at a Solution

Using summation, I set the static friction force equal to the centripetal force for equilibrium and solved for $\omega$.
$\omega = \sqrt{{\mu_s g}/{r}}$

 

[PeterO]

Homework Statement

"If the coefficient of static friction between the block of mass m and the turntable is $\mu_s$, determine the maximum constant angular velocity of the platform without causing the block to slip." I'm actually using this problem to understand why I'm getting the wrong answer to another question, unfortunately the book doesn't actually say if I have the right answer to THIS one. r is the radius, of course.

Homework Equations

$f = \mu_s F_{n}\ F = m r \omega^2 \ \sum F = F_1 + F_2 F_{n} = m g$

The Attempt at a Solution

Using summation, I set the static friction force equal to the centripetal force for equilibrium and solved for $\omega$.
$\omega = \sqrt{{\mu_s g}/{r}}$

That final expression looks OK.

 

[Xamien]

Thanks!