Accelerating a Uniform Sphere Down an Incline

[physikx]

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)

 

[ehild]

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

 

[physikx]

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

 

[ehild]

You are welcome.

ehild