Conservation of angular momentum on low-friction bearings

In summary, the two disks, with rotational inertias of 3.3 kg m^2 and 6.6 kg m^2, respectively, are set spinning at 450 and 900 rev/min, and then coupled together. The final angular speed of the coupled disks can be found by applying the principle of conservation of angular momentum, where the total angular momentum is the sum of the individual angular momenta of each disk.
  • #1
Seraph404
64
0

Homework Statement



Two disks are mounted on low-friction bearings on the same axle and can be brought together so that they couple and rotate as one unit. a) The first disk, with rotational inertia 3.3 kg m^2 about its central axis, is set spinning at 450 rev/min. The second disk, with rotational inertia 6.6 kg m^2 about its central axis, is set spinning at 900 rev/min in the same direction as the first. They then couple together. What is their angular speed after coupling?



Homework Equations



L = L'
L = Iw



The Attempt at a Solution



Can I get some hints on how to find the final rotational inertia? I'm sure it's something simple; I've just sort of been struggling with this chapter. I can't seem to visulize angular momentum at all.
 
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  • #2
Seraph404 said:
Can I get some hints on how to find the final rotational inertia?
The rotational inertia of the coupled disks is just the sum of the individual rotational inertias of each disk.
 
  • #3
Then what is the initial rotational inertia?
 
  • #4
Seraph404 said:
Then what is the initial rotational inertia?
The rotational inertia of each disk is given.

Hint: The total angular momentum is the sum of the angular momenta of each disk. (I suspect that's the question you meant to ask.)
 
  • #5
Oh I see. I feel dumb, now.
 

1. What is conservation of angular momentum?

The conservation of angular momentum is a fundamental law of physics that states that the total angular momentum of a system remains constant unless acted upon by an external torque. This means that in a closed system, the amount of angular momentum will remain the same, even if individual objects within the system may experience changes in their angular momentum.

2. How does conservation of angular momentum apply to low-friction bearings?

In low-friction bearings, the angular momentum of the wheel or axle is conserved due to the small amount of friction present. This means that the wheel or axle will continue to spin at a constant angular velocity, unless acted upon by an external torque. This is why low-friction bearings are used in various applications, such as bicycles and vehicles, to minimize the loss of energy due to friction.

3. What factors can affect the conservation of angular momentum on low-friction bearings?

The main factor that can affect the conservation of angular momentum on low-friction bearings is the presence of external torques. These can come from various sources, such as air resistance, friction from the ground, or other forces acting on the system. Additionally, any changes in the mass or distribution of mass within the system can also affect the conservation of angular momentum.

4. How is the conservation of angular momentum on low-friction bearings used in practical applications?

The conservation of angular momentum on low-friction bearings is used in numerous practical applications, ranging from transportation to industrial machinery. For example, in vehicles, low-friction bearings are used in the wheels to reduce energy loss and improve efficiency. In industrial machinery, low-friction bearings are used to minimize wear and tear on moving parts and reduce the need for frequent maintenance.

5. Can the conservation of angular momentum on low-friction bearings be violated?

No, the conservation of angular momentum is a fundamental law of physics and cannot be violated. In a closed system, the total angular momentum will remain constant, and any changes in the angular momentum of individual objects can be explained by external torques acting on the system. However, in open systems, such as those with external forces or torques acting on them, the conservation of angular momentum may not hold true.

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