# Rotation: Speed of an object as it slips off a rotating disk

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

A [itex]75g[/itex] mass sits [itex]75cm[/itex] from the center of a rotating platform undergoing a uniform angular acceleration of [itex] 0.125rad/s [/itex]. The coefficient of static friction between the mass and the platform is [itex]0.250[/itex]. What is the speed of the mass when is slides off?

A. 0.889 m/s

B. 1.26 m/s

C. 1.44 m/s

D. 1.58 m/s

E. It will never slide off

I’m also given an image of a disk with a mass on it, and the mass is located at the edge of the disk a distance r from the center.

My variables as far as I can tell:

α=0.125rad/s^{2}

m=75g

r=.75m

g=9.8m/s^{2}

**2. Relevant equations**

∑F_{x}=f_{s}=ma_{r}

∑F_{y}=N-mg=0

f_{s}=μ_{s}N

a_{r}=ω^{2}r

a_{t}=αr

I’m not sure if there are other equations I need in order to solve this problem

**3. The attempt at a solution**

I set up a free body diagram using the sum of the forces in the x and y directions:

∑F_{x}=f_{s}=ma_{r}

∑F_{y}=N-mg=0

I solved for f_{s}=μ_{s}mg

I replaced a w/ ω^{2}r to get ∑F_{x}=μ_{s}mg=mω^{2}r

Then I solved for ω to get [itex]ω=\sqrt{μg/r}=\sqrt{\frac{(.25)(9.8)}{.75}}[/itex]. This gave me an answer of [itex]1.807rad/s[/itex] which isn’t close to any of the given answers.

I’m also unsure because I didn’t actually use the value for the angular acceleration. I thought that by solving the problem how I did I would be able to find the maximum speed the object would be able to rotate on the disk without slipping, and any values greater than that would cause the object to slide and fall off. I’m struggling with this problem and I don’t know if I’m even starting correctly.

http://ift.tt/NXcqq1

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