Angular speed of a disk, given a force

[zalnas]

Homework Statement

A uniform-density 7 kg disk of radius 0.27 m is mounted on a nearly frictionless axle. Initially it is not spinning. A string is wrapped tightly around the disk, and you pull on the string with a constant force of 45 N through a distance of 0.9 m. Now what is the angular speed?

Homework Equations

K_rot = .5*I*omega²
I_disk = .5*m*R²
K = .5*m*v²
where I is the moment of intertia

The Attempt at a Solution

I've attempted setting K_rot equal to the force applied times the distance over which it is applied. I then plugged in I using the given information, and solved for the period from the K_rot equation.

 

[Mindscrape]

I think it will help you to realize a couple equations relating to torque

$$\tau = I \frac{d \omega}{dt}$$
$$\tau = \mathbf{r} \times \mathbf{F}$$

Though I am not entirely sure what the problem means by "and you pull on the string with a constant force of 45 N through a distance of 0.9 m" maybe you will and you will be on your way ;)

 

[zalnas]

Thanks for the reply.

I tried setting the two equal:
.5*7*.27² d$$\omega$$/dt = .27*45

Which yielded 47.62 m/s. However, that isn't the correct answer.

 

[Mindscrape]

Oh wait, my bad, I know what the line is alluding to now. Sorry for leading you astray. Yeah, you had the right idea before.

$$W=Fd$$
$$Krot=.5I\omega^2$$

Work energy theorem ought to work pretty well here. Seems you did that, so why did you solve for the period? Solve for angular velocity.

 

[zalnas]

Ah, I'm not sure why I solved for the period. I got the correct answer, thank you very much!