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**Given**

A puck of mass m on a merry-go-round (a flat rotating disk) has constant angular velocity [tex]\omega[/tex] and coefficient of static friction between the puck and the disk of [tex]{\mu}_{s}[/tex].

**Task**

Determine how far away from the center of the merry-go-round the hockey puck can be placed without sliding.

**Solve**

here's my attempt at a solution:

we want the puck to have zero velocity, so that when we integrate velocity with respect to time we get out a constant k, which is our radius from the center.

for the general case:

[tex]F = ma_{f} = m\ddot{R}_{f} + ma_{r} + m\dot{\omega} \times r + 2m\omega \times v_{r}[/tex]

the only force internal to the inertial reference frame is the friction force [tex]m\mu_{s}g[/tex]

and are solving for r for the zero velocity case and constant angular velocity, we can throw out the first two terms as well as the last:

[tex]F = m\mu_{s}g = m\dot{\omega} \times r [/tex]

which allows to say

[tex] m\mu_{s}g = mr\omega^{2} \hat{i}[/tex]

solving for r:

[tex] \frac{\mu_{s}g}{\omega^{2}} = r \hat{i}[/tex]

i feel really shaky about this result because i just dont feel confident about it because a) the thorton and marion book is too high-level and relies too heavily on mathematical formalism which b) i suck at.

any help or comments would be appreciated.