Solving Solid Disk Rolling Up Incline: Find Height h

[NathanLeduc1]

Homework Statement

A solid disk of mass m and radius R rolls without slipping with a velocity v. Assuming it doesn't slip, how far vertically will it roll up an incline?

Homework Equations

I=0.5mr²
E=0.5Iω²
KE=0.5mv²
PE=mgh

The Attempt at a Solution

I'm thinking that we need to find the height h when the kinetic energy is converted to potential energy. So:
0.5Iω²+mv²=mgh
0.5*0.5mr²ω²+mv²=mgh
0.25r²ω²+v²=gh
h=(0.25r²ω²+v²)/g
Is that right? I feel weird because I still have ω in there.

 

[SammyS]

Homework Statement

A solid disk of mass m and radius R rolls without slipping with a velocity v. Assuming it doesn't slip, how far vertically will it roll up an incline?

Homework Equations

I=0.5mr²
E=0.5Iω²
KE=0.5mv²
PE=mgh

The Attempt at a Solution

I'm thinking that we need to find the height h when the kinetic energy is converted to potential energy. So:
0.5Iω²+mv²=mgh
0.5*0.5mr²ω²+mv²=mgh
0.25r²ω²+v²=gh
h=(0.25r²ω²+v²)/g
Is that right? I feel weird because I still have ω in there.

What's the relationship between v and ω ?

 

[NathanLeduc1]

Ah, either you're a genius or I'm dumb. Probably both. Thank you.

I got a final answer of (1.2*v^2)/g = h.

 

[NathanLeduc1]

Oops, 1.25... ((5/4)(v^2))/g = h

 

[SammyS]

Ah, either you're a genius or I'm dumb. Probably both. Thank you.

Probably neither.

I considered a lengthier reply to your Original Post, but then though I'd see what you could do with a fairly subtle hint/question. From that, you completed the exercise. I commend you for that.

You might be surprised at how many people need to be led by the nose, step-by-step to an answer.

I got a final answer of (1.2*v^2)/g = h.