# Rate of rotation and inertia (prevent homicide and help me, please)

1. Apr 22, 2005

### NoHeart

i understand 4 of the 6 problems on this week's online physics quiz, but this one is driving me completely NUTS!

a diver rotates at 1 revolution per second in the stretched out position. when the diver tucks her head in and bends her legs, assume her length is shortened by 1/2. what is her rate of rotation in this position?
my choices are 4 Hz or 5 Hz, you'd think having only 2 choices would make this easier, but alas, i am dumbfounded.

i have tried thinking of the diver in the stretched out position as a rod, with rotational inertia 1/12ML^2
the other position would be like a solid sphere, with rotational inertia 2/5MR^2

1 revolution per second is 1 Hz, or 2pi r/s

the angular momentum (which may be irrelevant) of the stretched out position is
L= 1/12M(2r)^2 * 6.28 radians/1 revolution * 1 revolution/1second
this leaves me with L=2.093Mr^2 rad/sec

L of ball position is

slowly going insane, i see that rotational accleration = net torque/rotational inertia

any help, hints, or a slap across the face would be greatly appreciated

(p.s.- anyone else think online physics is the STUPIDEST idea EVER?)

2. Apr 22, 2005

### cepheid

Staff Emeritus
*Slaps NoHeart in the face*, "wake up man!"

Lol...just kidding. :tongue2:

Keep in mind these quizzes never have super complex questions, they are always just testing the basic concepts. In this case, angular momentum, L, can be expressed as:

$$L = I\omega$$

Where I is the moment of inertia. Keep it simple, model the diver as having the same overall shape, whether she's fully extended or not. After all, they only give you length, $l$, to work with. So if:

$$I \propto l^2$$

then when $l$ is halved, by what factor does I decrease? _________

But if I decreases by that factor, and by conservation of angular momentum, the product $L = I\omega$ must remain constant, then by what factor does $\omega$ increase to compensate?

Yes, I also feel that online physics quizzes are a stupid idea.

3. Apr 22, 2005

### NoHeart

1/4! i love you!
and i wish it were only the quizzes that are online, but it's the whole class- the online "lectures" are simply outlines of the chapters in the book, and the book is completely useless when it comes to the quizzes and tests. i have been teaching myself all of the concepts involved in the class so far, with the help of many physics sites and this here amazing message board. if i had found this board at the beginning of the quarter, i'd probably have an A instead of a B.