Why Does a Sphere Start Skidding on a Dome at a 30 Degree Angle?

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SUMMARY

A uniform solid sphere begins to skid on a spherical dome at a critical angle of 30 degrees due to the balance of forces acting on it. The skidding occurs when the gravitational force component exceeds the static frictional force at this angle. To calculate the coefficient of static friction, one must analyze the forces using Newton's second law and derive the expression for the sphere's acceleration while rolling down the dome.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Knowledge of static friction and its coefficient
  • Familiarity with free body diagrams
  • Basic concepts of rotational motion and rolling dynamics
NEXT STEPS
  • Study the derivation of the coefficient of static friction in rolling motion
  • Learn how to construct and interpret free body diagrams for dynamic systems
  • Explore the principles of rotational dynamics and moment of inertia
  • Investigate the effects of different surface materials on static friction
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in the dynamics of rolling motion and frictional forces.

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A uniform Solid Sphere, placed on top of a spherical dome, rolls down the dome with negligible initial velocity. The sphere sphere start to skid(sliding at the point of contact )when the angle( angle btw the line joining the centre of the dome to the centre of the sphere and the vertical) equal to 30 deg.
Calculate the coefficient of static friction between the sphere and the dome.
I really do not know how to start. Can comeone please help me?
 
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Start by drawing a free body diagram of the sphere on the dome, and applying Newton's second law.

What forces are acting? What is the expression for the acceleration of the rolling sphere?
 

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