Solid disk rolling

  • #1

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.
 

Answers and Replies

  • #2
SammyS
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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 ?
 
  • #3
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.
 
  • #5
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
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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.
 

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