Angluar Speed and Moment of Inertia

[brad_i2001]

Homework Statement

When 100 joules of work is done upon a flywheel, it's angular speed increases from 60 rpm to 180 rpm. What is the moment of inertia?

Homework Equations

Angular Acceleration = (Radius)(Angular Velocity)^2
I= 1/2MR^2
Work=FD

The Attempt at a Solution

To be honest, I am not sure how to apply work to either of the formulas. I know the Angular Acceleration is 120 rpm, but still do not know the radius. Would you substitute 120 for angular velocity and 180 for angular Acceleration? This would give the radius, and the mass would be found by the W=FD formula.

-Thanks!

Homework Statement

A 10 g ball is thrown straight down from a height of 2 meters. If the ball strikes the floor at a speed of 7.5 m/sec, what is the initial speed of the ball?

Homework Equations

dy= -2
vi=?
dx=(vx)(t)
dy=-1/2gt^2

The Attempt at a Solution

That is as far as I have gotten. I am, once again, not sure how to apply the formula to the given information. I am sure this one is much easier than the last, but I still need help.

-Thanks!

 

[foxjwill]

You can do this in terms of energy. $$K_{r0} + W = K_{r}$$ where $$K_r = \frac{1}{2}I\omega^2$$. Also, just as a side note, centripetal acceleration is $$r\omega^2$$, angular acceleration is $$\frac{d\omega}{dt}$$.

 

[brad_i2001]

Thank you SO Much! Everything worked! Do you have any suggestions for the falling ball question? Thanks Again!

 

[Doc Al]

For the falling ball problem, use the complete kinematic equation for vertical displacement:

$$y = y_0 + v_0 t - (1/2) g t^2$$