How Many Revolutions Before the Mass Slips on a Rotating Disk?

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To determine how many revolutions a mass will make on a rotating disk before slipping occurs, one must analyze the forces acting on the mass, particularly the static friction and centripetal force. The mass experiences a static friction force of 0.075 N, and the disk has a constant angular acceleration of 0.80 rad/s². The key is to find the angular velocity at which the centripetal force exceeds the frictional force. Once the critical angular velocity is established, the angular displacement can be calculated to find the total number of revolutions. Understanding these dynamics is essential for solving the problem effectively.
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Homework Statement


A 25gm mass sits on the surface of a circular disk 10 cm from the center of the disk. The force of static frictio nbetween the mass and surface of the disk is 0.075 N. The disk is initially at rest, but then experiences a constant angular acceleration of 0.80 rad/s^2. How many revolutions will the disk make before the mass starts to slip outward?


Homework Equations


i'm not exactly sure what equation to use-which is why I'm here...


The Attempt at a Solution


(.80rad) (1 rev) ...= 1.3rev/s
...5^2...2\pirad

i don't know ehre to go from here...
 
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Consider the centripetal acceleration on the mass. At what ω then will the centripetal force on the mass overcome the friction that maintains it in position?

Once you know ω, you can then determine the angular displacement.

Maybe this link would be helpful:
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#rlin
 

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