# Homework Help: Angular velocity and acceleration

1. May 25, 2016

### Nikstykal

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
ar=v2/r
ar=r''-rθ'2
aθ=rθ''+2r'θ'
ΣFi=mai
Ff,max=μN

3. The attempt at a solution
I first set up a free body diagram with wmass pointing downwards, Ff pointing left, normal pointing upwards, with ar 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=t2+ct+d

ΣFz=maz=N-mg, since az=0, N=mg
ΣFr=mar=m(r''-rθ'2)=-Ff
Combining: m(r''-rθ'2)=-μmg
Simplifying: -rθ'2=-μg

θ' = ω = √(μg/r)
θ' = √(0.2⋅(9.81m/s2)/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.

2. May 25, 2016

### rpthomps

That seems right to me. although the acceleration is to the left (which the math seems to identify with already)