# AP Physics C rotational Energy

1. A uniform solid sphere of radius r starts from rest at a height h and rolls without slipping along the loop-the-loop track of radius R as shown.
a) What is the smallest value of h for which the sphere will not leave the track at the top of the loop?

Attempt:

## Homework Equations

$$\Delta$$PE = mgh - 2mgR
$$\Delta$$KE = 1/2 mv2 + 1/2 Iw2
ac = v2/R
v = rw

## The Attempt at a Solution

mgh = 2mgR + 1/2 Iw2 + 1/2 mv2
I = 2/5 mr2
mgh = 2mgR + 1/5 mr2w2 + 1/2 mv2
N = mg - mac = mg - mv2/R = 0
v2 = gR
mgh = 2mgR + 1/2 mv2 + 1/5 mv2 +2mgR = 2.7mgR
h = 2.7R

however, this answer is wrong, and the correct one is h = 2.7R - 1.7r. can anybody correct me on this?