# What is its linear speed at the bottom of the incline?

## Homework Statement

A spherical object with a moment of inertia of 0.584mr2 starts from rest rolling down a 2.25-m high incline. If the sphere is rolling without slipping

## Homework Equations

I the best equation to use for this problem is k(initial)+u(initial)=k(final)+u(final)

## The Attempt at a Solution

I stretch the equation 1/2mv^2(initial)+1/2Iω^(initial)+mgh(initial)=1/2mv^2(final)+1/2Iω^2(final)+mgh(final).

since the object started from rest the initial kinetic energy and the final potential energy is zero, which leads me to this equation

mgh(initial)=1/2mv^2(final)+1/20.584mr^2ω^2(final). As I continue reduce the equations I round up with this.

gh(initial)=0.792v^2(final)

v=sqrt(9.81m/s^2)(2.25m)/0.792

the linear speed I came up with was 5.279m/s.

Did I do this right?

haruspex
Homework Helper
Gold Member
2020 Award
v=sqrt(9.81m/s^2)(2.25m)/0.792
The parentheses aren't written correctly there, but the method's fine and I agree with your final answer.

The parentheses aren't written correctly there, but the method's fine and I agree with your final answer.

How would I write the parentheses the correct way?

haruspex