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

AI Thread Summary
A uniform solid sphere begins to skid on a spherical dome at a 30-degree angle due to the balance of forces acting on it. To analyze this, one should start with a free body diagram to identify the gravitational force, normal force, and frictional force at play. The expression for the acceleration of the rolling sphere can be derived using Newton's second law, considering both translational and rotational motion. The coefficient of static friction can then be calculated based on the conditions at which skidding occurs. Understanding these dynamics is crucial for solving the problem effectively.
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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 verticle) 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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