Accelerating a Uniform Sphere Down an Incline

AI Thread Summary
To find the acceleration of a uniform sphere rolling down a 30-degree incline, start with the potential energy equation, mgh, and the kinetic energy equations for both translational and rotational motion. The initial kinetic energy is zero since the sphere starts from rest. After calculating the velocity at the end of the slope, use the relationship s = v^2/(2a) to determine the acceleration of the center of mass. The discussion highlights the importance of correctly applying energy conservation principles and understanding the motion equations to solve for acceleration.
physikx
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Homework Statement


A uniform sphere rolls down a 30 degree incline θ from height h. Initially, the solid is at rest. Find the acceleration for the center of the mass of the solid.

I am not sure where to start with this problem. I started with the energy formulas, but I am not sure how to find the acceleration of the center of mass from there. I just need a guide on what formulas or setup to use, thanks!

Homework Equations


Translational and rotational motion equations

The Attempt at a Solution


K_i=mghsin30
K_f=1/2mv^2+1/2Iω^2

then I solved for v:
v=radical(10/7*ghsin30)
 
Last edited:
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Hi, physikx,

The potential energy is mgh (h is the height of the (slope). Correct your result for v.

V is the speed of the CM at the end of the slope. Find the length travelled, and use the relation s=v^2/(2a) to determine the acceleration of the CM.

ehild
 
Hey ehid,

Thank you so much for the help! I was able to setup the problem and get the answer. I really appreciate the guidance.

Peace
 
You are welcome.

ehild
 

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