MOMENTS AND TORQUES

Why is this topic of significance to XMM?

     If we didn't have torques we wouldn't have angular momentum. Without angular momentum we wouldn't have circular motion. Without circular motion we would not have orbits. Without orbits we wouldn't have XMM. And even if we did have XMM we would have very little to look at and what there was would be very uninteresting because we wouldn't have planetary systems, galaxies or clusters of galaxies. Moments and torques are essential not only to XMM but for the whole of astrophysics.

What are moments and torques?

     Whenever we talk about a mass undergoing circular motion we need some reference to define the point about which the circular motion is taking place or can take place. Let us take this fixed point to be O and consider a mass m at some distance from O. If a force F is applied to the mass in the direction of O then a linear acceleration occurs and there will be an increase in the linear momentum of the mass. If the force is not in the direction of O then an angular acceleration results and angular momentum is imparted to the mass. (To make this actually work we need the mass to be "connected" to O in some way through a central force such as a gravitational force or the tension in a string)

In this case the force on the mass is directed towards o, and so the mass moves straight towards this point.

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In this second case the force is not directed straight towards o. This example shows what would happen if the mass, m, was gravitationally attracted by some object at o and a force was imparted upon it.

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     In the case where the force is not towards O we can break the force down into its two components and represent the situation as