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

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SUMMARY

The discussion centers on calculating the number of revolutions a rotating disk makes before a 25g mass slips off due to insufficient static friction. Given a static friction force of 0.075 N and an angular acceleration of 0.80 rad/s², the critical angular velocity (ω) must be determined to assess when the centripetal force exceeds the frictional force. The solution involves applying the equation for centripetal acceleration and angular displacement to find the total revolutions before slipping occurs.

PREREQUISITES
  • Understanding of centripetal acceleration and its formula
  • Knowledge of static friction and its role in rotational motion
  • Familiarity with angular kinematics, specifically angular displacement and acceleration
  • Basic grasp of Newton's laws of motion as they apply to rotating systems
NEXT STEPS
  • Calculate the critical angular velocity (ω) using the formula for centripetal force
  • Determine the angular displacement required for the mass to slip using kinematic equations
  • Explore the relationship between angular acceleration and the number of revolutions
  • Review examples of similar problems involving rotating disks and friction
USEFUL FOR

Students studying physics, particularly those focusing on rotational dynamics, as well as educators seeking to illustrate concepts of friction and motion in circular paths.

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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[tex]\pi[/tex]rad

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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