Changing axis of a rotating wheel

In summary, the woman standing on a rotating disc with a rotating wheel in her stretched arms can change the orientation of the wheel from horizontal to vertical, causing a change in the torque and angular momentum. This task may be difficult, especially when the wheel is rotating quickly, and can be proven using equations from rotational dynamics such as torque and angular momentum.
  • #1
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Homework Statement


Imagine a woman standing on a rotating disc (D) with a rotating wheel in her stretched arms (se picture here: http://image.vandrermodlyset.net/rotation.jpg ). The wheel is oriented in a horizontal plane, with the rotating axis (W) of the wheel parallel to that of the rotating woman (O) – that is vertical. This situation is rather stable as long as the woman doesn’t get nausea or tired arms. In situation A: W = O = D.
Lets say that she would suddenly change the axis of the rotating wheel (W) so that it became horizontal (situation B), and the wheel would now be oriented in the vertical plane intersecting the axis of the woman (O and D). A point on the outer rim of the wheel would form a helix-shape as the woman rotates on the disk.
I know that this task (going from situation A to B) will be difficult, even more when the wheel rotates fast, but how can I prove this using equations from rotational dynamics.

Homework Equations


T (torque) = r X F
L (angular momentum) = r x p

The Attempt at a Solution


The torque of the rotating woman rotates vetor L of the wheel until it becomes parallel to W=O=D
 
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  • #2
. When the woman then changes the orientation of the wheel, the torque will have to change as well, since there is a moment of inertia connected to it. This means that in order for the woman to change the orientation of the wheel, she has to apply a force F at the point r of the wheel and generate a larger torque T. The angular momentum of the wheel will also have to be changed since it depends on the force applied.
 
  • #3
. In order to change the axis of the rotating wheel from vertical to horizontal, the woman would need to apply a torque in the direction perpendicular to both the original and final axis of rotation. This can be calculated using the equation T = r x F, where r is the distance from the axis of rotation to the point where the force is applied, and F is the force applied. The greater the distance and the force, the greater the torque needed to change the axis of rotation. Additionally, the angular momentum of the wheel would also need to be conserved, meaning the woman would need to exert a force to counteract the change in angular momentum caused by changing the axis of rotation. This would require a significant amount of energy and strength, making it a difficult task as mentioned.
 

Related to Changing axis of a rotating wheel

1. What is meant by the "axis" of a rotating wheel?

The axis of a rotating wheel refers to the imaginary line around which the wheel rotates. It is an important concept in understanding the motion and stability of rotating objects.

2. Why would someone want to change the axis of a rotating wheel?

Changing the axis of a rotating wheel can be useful in various applications, such as steering a vehicle or controlling the direction of a spinning object. It can also help to redistribute weight and balance the wheel for better stability.

3. How can the axis of a rotating wheel be changed?

The axis of a rotating wheel can be changed by applying a torque or force at a specific angle to the wheel. This can be done manually, such as turning a steering wheel, or through mechanical systems like gears and pulleys.

4. What factors affect the stability of a rotating wheel when its axis is changed?

The stability of a rotating wheel when its axis is changed depends on several factors, including the amount of torque or force applied, the distribution of weight on the wheel, and the speed of rotation. These factors can affect the wheel's center of mass and its ability to maintain a steady rotation.

5. Are there any potential risks or dangers associated with changing the axis of a rotating wheel?

As with any type of motion, there are potential risks or dangers associated with changing the axis of a rotating wheel. These may include loss of control or stability, uneven weight distribution leading to vibrations or wobbling, and potential damage to the wheel or its components. It is important to consider these risks and take necessary precautions when changing the axis of a rotating wheel.

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