Solving Angular Velocity Q: Find Wf for 2 Spinning Disks

[Cyrad2]

Here's the problem as written:

A disk with moment of inertia I1 rotates with angular velocity Wi about a frictionless vertical axle. A second disk, with moment of inertia I2 initially not rotating, drops onto the first disk. Since the surfaces are rough, the two eventually reach the same angular speed.

I am suppost to find the final angular velocity, Wf, of the two spinning disks after the first disk falls onto the scond, spinning disk.

This is what I've got so far:
The problem is from the conservation of angular momentum section of my textbook, so i figured I'd use:
I2*Wi = (I1+I2)Wf
after i solve for Wf(which is what i want to find) i get:
Wf = (I2*Wi)/(I1+I2)

Is this the correct way to go about solving this? I'm not getting the right numbers when I plug them in...

 

[Doc Al]

The problem is from the conservation of angular momentum section of my textbook, so i figured I'd use:
I2*Wi = (I1+I2)Wf
after i solve for Wf(which is what i want to find) i get:
Wf = (I2*Wi)/(I1+I2)

You made an error in writing the conservation equation. It should be:
$$I_1 \omega_i = (I_1 + I_2) \omega_f$$

 

[wais]

Yes, you are on the right track with using the conservation of angular momentum equation. However, there are a few things to keep in mind when solving this problem.

First, make sure you are using the correct values for the moment of inertia for each disk. The moment of inertia, I, is a measure of an object's resistance to changes in its rotational motion. It is given by the formula: I = mr^2, where m is the mass of the object and r is the distance from the axis of rotation. So, for the first disk, you would use I1 = m1r1^2 and for the second disk, you would use I2 = m2r2^2.

Secondly, when the two disks eventually reach the same angular speed, their moment of inertia will be combined. This means that instead of using I1 and I2 separately, you need to use the combined moment of inertia, I1+I2.

Finally, don't forget to convert all units to a consistent system (such as SI units) before plugging them into the equation.

If you are still having trouble getting the correct answer, double check your values and calculations to make sure they are accurate. Also, don't hesitate to reach out for help from your teacher or classmates if needed. Good luck!