Hollow sphere, angular momentum, torque problem? help?

[nchin]

Hollow sphere, angular momentum, torque problem? help??

a hollow sphere or radius 0.15m with rotational inertia = 0.040 kg m^2 about a line through its center of mass, rolls without slipping up a surface inclined 30 degree to the horizontal. at a certain initial position,the sphere's total kinetic energy is 20J.

a) How much of this initial KE is rotational?

what i did

Hollow sphere = 2/3MR^(2)
KErot = 1/2 Iω^2

KEtotal = KEtranslational + KErotational

a) 20 = 1/2mv^2 + 1/2 x 2/3 mr^2
20 = 1/2mv^2 + 1/3 mr^2

this part confuses me
1/2mv^2 + 1/3 mr^2 = 5/6mv^2
20 = 5/6mv^2

How was 1/2mv^2 + 1/3 MR^2 = 5/6mv^2?? mv and MR are different yet how were they both added together??

 

[haruspex]

When dimensions don't match up, backtrack to the first instance. It's here:

a) 20 = 1/2mv^2 + 1/2 x 2/3 mr^2

ω is missing.

 

[nchin]

When dimensions don't match up, backtrack to the first instance. It's here:

ω is missing.

1/2mv^2 + 1/2 x 2/3 mr^2ω = 5/6mv^2

ok so if i put a ω there, how would it still = 5/6mv^2? in other words how can you change mr^2ω into mv^2? help!

 

[nchin]

oh nvm i got it. w = V^2/R^2. r cancel out. thanks!