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## Homework Statement

Small mass sits on a circular revolving table, 200 mm from center. It is given a constant angular acceleration of 2 rad/s. The static coefficient of friction is 0.2. At what angular velocity will the mass start to slip?

## Homework Equations

a

_{r}=v

^{2}/r

a

_{r}=r''-rθ'

^{2}

a

_{θ}=rθ''+2r'θ'

ΣF

_{i}=ma

_{i}

F

_{f,max}=μN

## The Attempt at a Solution

I first set up a free body diagram with w

_{mass}pointing downwards, F

_{f}pointing left, normal pointing upwards, with a

_{r}vector pointing to the right.

Since the distance is unchanging, r = 0.2m, r'=0, r''=0. θ''=2rad/s, θ'=2t rad/s + c, θ=t

^{2}+ct+d

ΣF

_{z}=ma

_{z}=N-mg, since a

_{z}=0, N=mg

ΣF

_{r}=ma

_{r}=m(r''-rθ'

^{2})=-F

_{f}

Combining: m(r''-rθ'

^{2})=-μmg

Simplifying: -rθ'

^{2}=-μg

θ' = ω = √(μg/r)

θ' = √(0.2⋅(9.81m/s

^{2})/0.2m) = 3.13 rad/s

Does this look correct? I never used the given angular acceleration so I feel like I missed something. Thank you.