Deriving RPM for Object Slipping from Rotating Surface

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SUMMARY

The discussion focuses on deriving the expression for rotations per minute (RPM) of a rotating surface at the critical point when an object with mass M1 begins to slip. The critical rotation rate is reached when the tangential acceleration becomes significant enough to overcome the static friction holding the object in place. Key forces involved include the gravitational force acting on the object and the frictional force opposing the motion. Understanding these dynamics is essential for calculating the RPM at which slipping occurs.

PREREQUISITES
  • Newton's laws of motion
  • Concept of tangential acceleration
  • Static friction and its role in motion
  • Basic rotational dynamics
NEXT STEPS
  • Study the relationship between tangential acceleration and rotational motion
  • Learn about the equations governing static friction
  • Explore the derivation of critical rotation rates in rotating systems
  • Investigate the effects of mass distribution on rotational stability
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of rotating systems and frictional forces.

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Homework Statement



A object(have mass M1) is placed at a R1 distance from the center of a horizontal surface that can rotate. The surface rotation is very FAST INCREASE ( tangential acceleration is non-negligible) until the surface reaches a cirtical rotation rate. At that instant, the object begins to slip with respect to the surface. Derive an expression for number of rotation per minute made by the surface at this critical time.
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Homework Equations


The Attempt at a Solution


I have no idea...Can somebody give my a hint? thank you
 
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What holds the block in place? What forces are operating? What are their directions?
 

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