Help With Physics Homework Please I'm Desperate

[luvtodance151]

Homework Statement

I am having trouble with two problems.

1. An onion grown in 1994 had a record breaking mass of 5.55 kg. Assume that this onion can approximated by a uniform, solid sphere. Suppose the onion rolled down the inclined ramp that had a height of 1.40 m. What was the onion's rotational kinetic energy? Assume that there was no slippage between the ramp and the onion's surface.

2. The longest spacewalk by a team of astronauts lasted more than 8 h. It was performed in 1992 by 3 crew members from the space shutttle Endeavour. Suppose that during the walk 2 astronauts with equal masses held the opposite ends of a rope that was 10 m long. From the point of view of the 3rd astronaut, te other 2 astronauts rotated about the midpoint of the rope with an angular speed of 1.26 rad/s^2. If the astronauts shortened the rope equally from both ends, what was their angular speed when the rope was 4 m long?

Homework Equations

1. I know that the formula to use is 1/2(I)(final angular velocity)^2

2. I have no idea what to do here

The Attempt at a Solution

1. I'm having problems finding the final angular velocity because I don't have a time.

2. Once again, no idea what to do.

 

[Dick]

Let's just do 1) first, ok? When you reach the bottom of the ramp you know the total kinetic energy from mgh, right? Part of it is rotational and part is linear. But since you know there is no slipping, you know the relation between the rotational velocity and the linear velocity, don't you? Equate the sum to mgh.

 

[luvtodance151]

Nope we didn't learn the relation between the rotational velocity and linear velocity. Sorry our teacher is really bad and doesn't teach us anything...

 

[Dick]

If you have a bad teacher, you have to learn to survive it by doing work on your own. You can't let one bad teacher doom your career. v=r*omega. That's usually the formula giving velocity at the rim of a rotating hoop with a stationary center. Draw a picture and figure out why it also works to relate the velocity of center to angular rate of rotation when there is no sliding.

 

[luvtodance151]

Thanks for the help, I think I've got it now.
And trust me, I'm not letting one bad teacher ruin my career. I've survived the whole year so far. And most of the time I end up helping other people in my class, not to mention I have one of the few A's in the class. So I think I've done pretty well considering the circumstances.