Explaining Precession with Angular Momentum & Torque

[JolleJ]

Homework Statement

I'm trying to describe the physical phenomena precession using vectors. I need to explain, why a bicycle wheel, which is spinning in the x-y-plane, and only held up in one of the sides, will start do a spin in the x-z-plane.

Homework Equations

Using Angular Momentum and Torque; explain the phenomena precession.

The Attempt at a Solution

I understand that gravity and the position vector together creates a torque. This of course change the angular momentum over time. With a simple spin, the angular momentum points along the x-axis. The torque creates a change in the angular momentum along the z-axis. This results in a total angular momentum, which is the sum of the original and the change of angular momentum. This of course changes things a bit. And I can see, why making the wheel turn, so that it is orthogonal on the angular momentum i a solution. However, I cannot see, why this is the only solution to the problem? Why is this exactly what happens? I mean, the angular momentum is defined as a cross product, so there must an indefinite amount of solutions to problem; so why is it that it is exactly the solution, where the wheel turns that is the one that happens?Thanks in advance.

 

[anathema]

The phenomenon of precession can be explained using the concepts of angular momentum and torque. In the case of a bicycle wheel spinning in the x-y plane and only held up on one side, the torque created by gravity on the wheel causes a change in its angular momentum. This change in angular momentum results in a total angular momentum that is a combination of the original angular momentum and the change caused by the torque.

Now, why does the wheel start to spin in the x-z plane? This is because the only way for the total angular momentum to remain constant is if the wheel starts to spin in the direction of the torque, which is along the z-axis. This is the only solution that satisfies the conservation of angular momentum.

You are correct in stating that there may be an indefinite amount of solutions to this problem, but the one that actually occurs is the one that satisfies the laws of physics. In this case, it is the solution where the wheel starts to spin in the x-z plane.

I hope this explanation helps you understand the phenomenon of precession better. If you have any further questions, please feel free to ask. As scientists, it is our job to explore and understand the natural world, and I am happy to assist you in any way I can.

 

[ogb p]

Precession is a phenomenon that occurs when a spinning object experiences a torque that causes its axis of rotation to change direction. This can be explained using the concepts of angular momentum and torque.

First, let's consider the bicycle wheel spinning in the x-y plane. The wheel has an angular momentum vector that points along the x-axis. When the wheel is held up on one side, it is subjected to a torque created by the force of gravity acting on the wheel's center of mass. This torque is perpendicular to both the angular momentum vector and the position vector of the wheel's center of mass, causing a change in the direction of the angular momentum.

This change in angular momentum causes the wheel's axis of rotation to start precessing, or rotating, in the x-z plane. This is because the total angular momentum of the wheel is now the sum of the original angular momentum vector and the change in angular momentum caused by the torque. This new angular momentum vector is now tilted in the x-z plane, causing the wheel to precess around the z-axis.

But why does the wheel precess in the x-z plane instead of any other plane? This can be explained by the fact that the torque created by gravity is always perpendicular to the position vector of the wheel's center of mass. This means that the torque always causes a change in the direction of the angular momentum vector, which in turn causes the wheel to precess around a perpendicular axis.

In the case of the bicycle wheel, the only perpendicular axis to the x-axis is the z-axis. Therefore, the wheel will precess around the z-axis when subjected to a torque from gravity. This is why the solution where the wheel turns to become orthogonal to the angular momentum vector is the only one that happens.

In summary, the concepts of angular momentum and torque can explain why a spinning object, such as a bicycle wheel, will precess when subjected to a torque. The specific direction of precession is determined by the direction of the torque and the initial angular momentum vector.