Question

PLEASE HELP. I SWEAR TO EVERY GOD THAT THIS ISN'T HW. I AM JUST LOST, HELP A BROTHA OUT.
A small piece of cheese is placed at the center of a thin horizontal 2 kg rod
of length L. The rod rotates horizontally around its center of mass with an
angular velocity 10 rad/sec as shown in the figure. A 0.5 kg mouse originally
standing at the edge of the rod runs towards the cheese. What is the angular
velocity (in rad/s) of the rod when the mouse reaches the cheese?

Answer 1

try to apply conservation of angular momentum

Answer 2

I guess I can try, but I am pretty lost with this problem :(

Answer 3

what is angular momentum of the system in the beginning, before mouse starts to move?

Answer 4

is it equal to the angular velocity? 10 rads/sec?

Answer 5

I'm sorry that's probably wrong I feel so stupid rn ugh

Answer 6

NP. you know momentum right?
\[P=mv\]
angular momentum is similar to that, except true for rotating objects
\[L=I\omega\]

Answer 7

conservation of angular momentum, basically
\[L_{initial}=L_{final}\]

Answer 8

Okay, I think I might be recalling this info

Answer 9

do you know what is \[I\]

Answer 10

I= 20

Answer 11

how did you get that?

Answer 12

I really have no idea tbh

Answer 13

Sorry

Answer 14

It is called moment of inertia, it depends shape of the object and rotation axis.
for rod rotating on its center
\[I=\frac{1}{12}ML^2\]
from
http://en.wikipedia.org/wiki/List_of_moments_of_inertia
for point object it is
\[I=mr^2\]

Answer 15

WOW okey

Answer 16

so initially you have rod and mouse on the edge which is point at \[r=L/2\]
at the end mouse move to the center and r becomes zero.

Answer 17

\[(\frac{ML^2}{12}+m(L/2)^2)\omega_0^2=\frac{ML^2}{12}\omega^2\]

Answer 18

thank you so much for this.

Answer 19

you are welcome, good luck

Answer 20

@bourne13. I actually have the answer to this problem available to me. This is actually an old exam problem from my Physics class at UF. Using your method, I was unable to get the correct answer.

I honestly thought that your method was sound, so I'm confused as to why it isn't producing the right answer. I've been struggling with this for a couple hours now!

Answer 21

center of the rod is fixed, :), right?

Answer 22

do you have the figure? I wonder if I missed something

Answer 23

It is, but it does rotate.

I actually tried a variation of your method before you posted, but I forgot to square both of the omegas. I had a eureka moment after I saw that you squared them, but like I said, it still didn't work out.

I'm not sure if you can access this or not, but it is question 16 on this site:
http://www.phys.ufl.edu/courses/phy2048/spring15/exams/2048_Fall14_Exam2.pdf

Answer 24

I am getting 140/3 rad/s

Answer 25

The answer is 17.5 rad/s. I keep getting 13.2.

Answer 26

In case you can't access the website, here's a rough drawing: