Calculating Acceleration of a Spherical Shell

AI Thread Summary
To calculate the acceleration of a hollow spherical shell rolling down a slope at an angle of 34.0 degrees, apply Newton's second law to both its translational and rotational motion. The friction force acts parallel to the slope, while gravity has a component acting down the slope. A free body diagram can help clarify the forces involved. The relationship between the translational acceleration and the rotational motion must be established to find the acceleration of the center of mass. Understanding these principles is essential for solving the problem accurately.
nurjamali
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A hollow spherical shell with mass 2.10 rolls without slipping down a slope that makes an angle of 34.0 with the horizontal.
Find the magnitude of the acceleration of the center of mass of the spherical shell.

I understood that the friction force is normal to the slope and there is a component of gravity in x direction(taking x-y plane at an angle of 34.0)
But I don't know the relation for calculating acceleration of the center of mass.
 
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The friction force is parallel to the slope.

To find the acceleration, apply Newton's 2nd law to both the translational and rotational motion of the shell.
 
Also, draw a freebody diagram to make things clearer to yourself..
 
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