How Does a Cockroach Affect Angular Velocity When Moving on a Disk?

[suspenc3]

a cockroach of mass m lies on the rim of a uniform disk of mass 10m that can rotate freely about its center like a merry go round. Initially the cockroach and disk rotate together with an angular velocity of $$\omega_0$$. Then the cockroach walks halfway to the center of the disk.

What is the change in \Delta \omega[/tex] in the angular velocity of the system?

I have no clue where to start...and no there are no numbers given.

Can some one help me/give me a hint?

 

[Pseudo Statistic]

You know that angular velocity = linear velocity v/r, the radius of the disk...
The cockroach's initial angular velocity would have been some value like v/10 (Because the radius is 10m)
I'm going to guess its angular velocity was the same when it was halfway through, in which case its angular velocity would be v/5...
The difference would be v/5 - v/10 = 2v/10 - v/10 = v/10
So the angular velocity would have gotten two times faster. (Assuming what I'm doing is right... which I'm unsure of)

 

[suspenc3]

but the radius is not 10...
mass of cockroach = m
mass of disk = 10m (10 times as much as cockroach)

 

[mezarashi]

When no numbers are given, assign variables and see if they cancel. You should apply the conservation of angular momentum principle

$$I_1\omega_1 = I_2\omega_2$$

The intertial moment is due to the disk and cockaroach. The disk's moment remains the same in 1 and 2. The moment of inertia of a point mass is $$I = mr^2$$.

 

[suspenc3]

so...how can I calculate everything if I don't have a radius?

 

[mezarashi]

As I've said, assign variables. Let the radius be anything R. Now continue to solve.

 

[yellow_river]

check the attached file

<< file with complete solution deleted by berkeman >>

 

[berkeman]

check the attached file

<< file with complete solution deleted by berkeman >>

Thank you for trying to help, yellow_river. But we do not provide complete solutions to Homework Help questions here on the PF. Please be tutorial in your help.