Angular Momentum of circular disk

[rms830]

Homework Statement

A flat uniform circular disk (radius = 2.50 m, mass = 1.00 102 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 55.0 kg person, standing 1.55 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 2.20 m/s relative to the ground.

Homework Equations

I have been using the definition of angular motion equation (L = I*omega)(I = mr^2) to try and find the resulting angular speed. What I am having trouble with is how to find L using the given numbers. I thought i read that L = r2, but putting those numbers into the equation has not given me the correct answer. The problem asks me to find the resulting angular speed, but since I have not been able to find L or omega, I haven't been able to solve.

Thanks.

 

[Doc Al]

Hint: Angular momentum is conserved. What's the initial angular momentum of the system before the person begins running?

 

[m2003]

Hello,

Thank you for sharing your question. It seems like you are on the right track with using the definition of angular momentum (L = I*omega) and the moment of inertia equation (I = mr^2) to solve this problem. However, it is important to note that the value of L is not equal to r^2, but rather it is the product of the moment of inertia and the angular velocity (L = I*omega).

In order to solve for the resulting angular speed, we need to first calculate the moment of inertia of the disk. Using the given radius and mass, we can plug those values into the moment of inertia equation (I = mr^2) to get a value of 1.00*10^5 kg*m^2.

Next, we need to calculate the angular momentum of the person running on the disk. We can do this by multiplying the person's mass (55.0 kg) by their tangential speed (2.20 m/s) and the distance from the axis (1.55 m). This gives us a value of 170.5 kg*m^2/s.

Now, we can set these two values equal to each other (L = I*omega) and solve for omega (angular speed). This will give us an angular speed of approximately 0.0017 rad/s.

I hope this helps and please let me know if you have any further questions. Good luck with your homework!