# Conservation of Angular Momentum and a Spinning Bicycle Wheel

• samirgaliz
In summary, angular momentum is conserved when the system is turned by an axis other than the z-axis.
samirgaliz
A person standing on a stationary friction-less turntable spins a bicycle wheel with the rotation axis of the wheel in the horizontal direction, thus the initial angular momentum is in the horizontal direction (x - axis), say to the right. Now suddenly the person turns the axis of rotation of the wheel by 90 degrees upward (final angular momentum of the wheel is now directed upward along the y- axis).

I understand that the initial angular momentum along the y- axis is zero. Thus we expect the final angular momentum of the system along the y- axis to be zero as well. So the person + platform will spin finally in the opposite direction of the spinning wheel.

But the problem I am having is with the initial x - component of angular momentum. How do we account for a final x- component of angular momentum? If there is no final angular momentum in the x- direction, then this means that angular momentum is not conserved! contradiction! Any help would be appreciated. Thanks.

There will be external forces acting on the system and so you should not expect angular momentum to be conserved in general.

Thanks Orodruin. I did think so but I can not figure out what the external torque is in this case.

The external torque comes from the axis of the turnable. The only direction it cannot provide a torque in is the y-direction (and hence the angular momentum in the y-direction is conserved).

If instead you fixed the entire system to rotate about a single point instead of an axis, then angular momentum with respect to that point would be conserved and the entire system would start spinning in the x-direction as well.

samirgaliz
Orodruin said:
The external torque comes from the axis of the turnable. The only direction it cannot provide a torque in is the y-direction (and hence the angular momentum in the y-direction is conserved).

If instead you fixed the entire system to rotate about a single point instead of an axis, then angular momentum with respect to that point would be conserved and the entire system would start spinning in the x-direction as well.
Orodruin said:
The external torque comes from the axis of the turnable. The only direction it cannot provide a torque in is the y-direction (and hence the angular momentum in the y-direction is conserved).

If instead you fixed the entire system to rotate about a single point instead of an axis, then angular momentum with respect to that point would be conserved and the entire system would start spinning in the x-direction as well.
Thank you.

Thank you Orodruin for you response. I am have difficulty visualising how this force is coming from the axis of the turntable. Any clarification would be appreciated.

## 1. What is conservation of angular momentum?

Conservation of angular momentum is a fundamental law of physics that states that the total angular momentum of a closed system remains constant, unless acted upon by an external torque. This means that the rotational motion of a system will remain unchanged unless an external force is applied.

## 2. How does a spinning bicycle wheel demonstrate conservation of angular momentum?

When a bicycle wheel is spinning, it has a certain amount of angular momentum. As long as there is no external torque acting on the wheel, this angular momentum will remain constant. This can be observed by the fact that the wheel will continue to spin even if the rider stops pedaling. This is because the rotational motion of the wheel is not affected by the rider's actions.

## 3. Can you explain the physics behind the conservation of angular momentum in a spinning bicycle wheel?

The conservation of angular momentum is a result of the law of inertia, which states that an object will remain in its state of motion unless acted upon by an external force. In the case of a spinning bicycle wheel, the angular momentum is created by the rotation of the wheel and this momentum will remain constant unless an external torque is applied.

## 4. How does the conservation of angular momentum apply to other objects besides a spinning bicycle wheel?

The conservation of angular momentum applies to all objects, not just spinning bicycle wheels. Any rotating object, such as a spinning top or a planet orbiting around a star, will exhibit this principle. It is a fundamental law of physics that applies to all rotational motion.

## 5. Can the conservation of angular momentum be violated?

No, the conservation of angular momentum is a fundamental law of physics that has been observed and tested numerous times. It has never been found to be violated. However, it is important to note that it only applies to a closed system, meaning that there are no external forces or torques acting on the system. In real-world situations, external forces can affect the angular momentum of an object, but the total angular momentum of the system will still remain constant.

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