- #1

roeb

- 107

- 1

## Homework Statement

A particle of mass m is moving on a frictionless horizontal table, attached to a massless string, the other end of which passes through a hole in the table. It was rotating with angular velocity [tex]\omega_0[/tex], at a distance [tex]r_0[/tex] from the hole. Assuming that I pull the string so slowly that we can always approximate the path of the particle at any time by a circle of slowly shrinking radius, calculate the work I did while pulling the string. Show that the work-energy theorem is satisfied in this case.

## Homework Equations

[tex]W = \int F . dr[/tex]

[/tex]\delta W = KE_f - KE_i[/tex]

## The Attempt at a Solution

Here is how I initially attempted the problem:

[tex]KE_i = \frac{1}{2}*m*(r_0 \omega_0)^2 [/tex]

[tex]KE_f = \frac{1}{2}*m*(r \omega_f)^2[/tex]

And by taking the difference I was hoping that I would get the work done. Unfortunately it turns out that I need to do something a bit more complicated.

I know [tex]W = \int F . dr[/tex] but I'm not really sure what to do in order to apply it to this situation.

Anyone have any hints?