# Sphere/disk rolling down an incline HELP

1. Nov 30, 2007

### asourpatchkid

Sphere/disk rolling down an incline HELP!!!

1. The problem statement, all variables and given/known data

a ball, or sphere with a radius of R and mass Mis rolling down an incline with a height of H and an angle of $$\Theta$$ how long does it take to get to the bottom

2. Relevant equations

Conservation of mechanical energy
Kf + Uf = Ki + Ui
K = 1/2 (I/R^2 + M)v^2

3. The attempt at a solution

i solved for the system with conservation of energy

1/2(I/R^2 + M )v^2 + 0 = 0 + Mgh

solved for final velocity of the ball or disc at the bottom of the incline

and got

v = [2gh/1 + ( I/ MR^2)]^0.5

set H=MG$$\Theta$$

and got

v = [2gMG$$\Theta$$/1 + ( I/ MR^2)]^0.5

i am having trouble however seeing how i can solve for time t in terms of all the variables.....please help!!!!!

2. Nov 30, 2007

### physucsc11

Well using the angle you can solve for the length of the incline in terms of height, and using that length you can find what the acceleration was using the formula
V(final)^2 = V(init)^2 + 2*a*(Xfinal- Xinit), with the velocity and length you found.
Then you can find the time using t = V/a