# Rotational accel to linear accel

1. Jun 24, 2009

### chloechloe

1. The problem statement, all variables and given/known data
I do not understand how a was solved for. the picture is a sphere rolling down a hill. Asked to solve for a.

2. Relevant equations
solve for a, use alpha = a/r
ma = mg sin theta - fs; T = fs*r = I*alpha = (2/5)mr^2; fs = (2/5)ma
a = (5/7)g sin theta

I can't see the progression through these steps

3. The attempt at a solution

2. Jun 24, 2009

### Staff: Mentor

(1) That's the condition for rolling without slipping.
(2) That's Newton's 2nd law applied to translation.
This is an attempt to apply Newton's 2nd law to rotation, but alpha was left out of the right hand term. It should be:
(3) T = fs*r = I*alpha = (2/5)mr^2*alpha
(4) Combine 1 and 3 to get this.
Combine 4 with 2 to get this.

3. Jun 24, 2009

### chloechloe

Thank you. Makes sense now. I was getting stuck at combining things at the end. The missing alpha didn't help either.

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