# Understanding spin

1. Feb 16, 2005

### FulhamFan3

It's my understanding that any acceleration is caused by a force. When you remove that force it goes at a constant velocity.

When an object is spinning it's accelerating, right? I mean the particles in the object are always changing direction. When left on it's own this leads me to beleive that eventually this should slow down. But that doesn't happen, it just keeps spinning at a constant speed. What force allows this system to keep accelerating.

If my understanding of this is completely wrong please tell me otherwise.

2. Feb 16, 2005

### Galileo

The individual particles of a rigid object spinning is space are accelerating, but the system as a whole is not.
The center of mass moves with a constant velocity.

The forces which cause the necessary centripetal force for the particles are constraint forces. These are always pointing towards the axis of rotation and thus do no work.

3. Feb 16, 2005

### Andrew Mason

An acceleration requires a force but not necessarily energy. If the force/acceleration is perpendicular to the direction of motion, there is no energy expended. In a spinning body, the forces are always central and the motion is always tangential, so no energy is required to keep it going. The centre of mass does not move as all forces are directed toward it equally from all directions.

AM

4. Feb 16, 2005

### vinter

Or stated otherwise, the centre of mass does not move because each particle pair contributes a pair of equal and opposite forces to the system (Newton's third law) as a result there is zero force acting on the system as a whole.

5. Feb 16, 2005

### ZapperZ

Staff Emeritus
There is also another way to look at this, which is even more FUNDAMENTAL than what has been described.

The emergence of Newton's Laws, especially F=ma, is actually a direct result of the conservation of linear momentum. That, in turn, is a manifestation of the translational symmetry of our universe [Aside: from Noether's theorem, every conservation law has a corresponding symmetry principle]. Thus, if you write F= dp/dt, and there is no net external force, then dp/dt = 0 and you have the conservation of linear momentum. This is where you get Newton's 1st Law and 3rd Law. Thus, Newton's Laws are simply the consequences of the conservation of linear momentum.

However, our universe or space is also isotropic (i.e. the same in every direction). This symmetry then results in the conservation of ANGULAR momentum L, i.e. dL/dt = 0. Again, if there's no external force or torque, the conservation law dictates that it will maintain its angular momentum. You will have the "angular" version of Newton's Laws being applied to such a system. They are idential to each other, because the identical conservation laws (and symmetry principles) are being applied.

Moral of the story here is that "F" isn't the key issue here. It is simply a consequence of a more fundamental principle. Once you understand where things come from and what is really the source for all this, you'll realize that there is a common root for many seemingly-different observations.

Zz.

6. Feb 17, 2005

### Andrew Mason

This is a very important and well stated point.

Force is often neither the simplest nor most illuminating way to approach classical mechanics. But, in human experience, the concept of 'force' is more intuitively understandable than conservation of linear and angular momentum. Conservation of angular momentum is very often counter-intuitive (eg. gyroscopic precession). That is probably why we prefer to use force.

Some have argued - eg. Hamilton, Feynman, - that the principle of 'least action' (which I have always had trouble with understanding conceptually, although it is readily understandable mathematically) is an even more fundamental way of approaching forces and motion: 'Forget about force. The path from A to B of a body is the path for which the integral of the difference between kinetic and potential energy - the 'action' - is least.' There is something mysteriously symmetrical and simple about the concept but I am afraid it escapes my intuition. So, unfortunately, I continue to think in terms of force (and conservation of energy and of linear and angular momentum).

AM