Ball rolling down an incline angular and linear acceleration

[Fascheue]

Homework Statement

A ball with moment of intertia bmr^2 rolls without slipping down a plane inclined at angle O. What is it’s linear acceleration?

Homework Equations

Fnet= ma

T = F x r

T = IO’’

a = rO’’

The Attempt at a Solution

Fnet = mgcos(O) - FfT = FfrT = IO’’

Ffr = bmr^2O’’

Ff = bmrO’’Fnet = mgcos(O) - BmrO’’a = O’’r

a/r = O’’Fnet = mgcos(O) - bma

ma = mg cos(O) - bma
a = gcos(O) - ba

a + ba = gcos(O)

a(1+b) = gcos(O)

a = gcos(O)/(1+b)

 

[Doc Al]

Fnet = mgcos(O) - Ff

Check this: What is the component of the weight parallel to the plane?

 

[Fascheue]

Check this: What is the component of the weight parallel to the plane?

Oops, would it be mgsin(O)?

I believe that would give an answer of gsin(O)/(1+b) following the rest of my steps.

 

[Doc Al]

Oops, would it be mgsin(O)?

Yep.

I believe that would give an answer of gsin(O)/(1+b) following the rest of my steps.

Looks good to me.