Moment of Inertia: Disk 1 & 2 Homework

In summary, the problem involves two disks with different moments of inertia and angular speeds. When the second disk falls onto the first, they rotate together with a new angular speed. To determine the moment of inertia of Disk 2, we can use the conservation of angular momentum, Iω = constant.
  • #1
Mia
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Homework Statement


In the diagram, Disk 1 has a moment of inertia of 4.40 kg · m2 and is rotating in the counterclockwise direction with an angular speed of 7.50 rad/s about a frictionless rod passing through its center. A second disk rotating clockwise with an angular speed of 9.50 rad/s falls from above onto Disk 1. The two then rotate as one in the clockwise direction with an angular speed of 1.40 rad/s. Determine the moment of inertia of Disk 2.

Homework Equations


L=Iω

The Attempt at a Solution


I have no idea how to start the problem.
 
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  • #2
Mia said:
I have no idea how to start the problem.
Any conservation laws you can think of that might apply?
 

1. What is the moment of inertia?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is a property that depends on the mass distribution of the object and the axis of rotation.

2. How is the moment of inertia calculated for a disk?

The moment of inertia for a disk is calculated using the formula I = (1/2)MR2, where M is the mass of the disk and R is the radius of the disk. This formula assumes that the disk has a uniform mass distribution.

3. How does the moment of inertia differ between Disk 1 and Disk 2?

The moment of inertia for Disk 1 and Disk 2 will be different because they have different masses and radii. However, if they have the same mass and radius, their moments of inertia will also be the same.

4. What is the significance of the moment of inertia for rotating objects?

The moment of inertia is important for understanding how objects rotate and how they respond to external forces. It can help in predicting an object's rotational motion and determining how much torque is needed to cause a change in its rotational speed.

5. How can the moment of inertia be affected by changing the mass or radius of the disk?

The moment of inertia is directly proportional to the mass and the square of the radius, so changing either of these will affect the moment of inertia. Increasing the mass or radius will increase the moment of inertia, while decreasing them will decrease the moment of inertia.

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