# Solid disk rolling

## 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?

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
Staff Emeritus
Homework Helper
Gold Member

## 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?

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 ?

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.

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

SammyS
Staff Emeritus