# Dark Matter, is it necessary?

1. May 31, 2005

### gaugeboson

Why is it necessary to assume dark matter exists in the universe? If we feel that galaxies are rotating faster than it is possible for normal matter to do so, they must have less moment of inertia. This will make their rotation fast. Hence, they should have less mass, not more!
I’ve heard that black holes finally evaporate. They then send out all the particles they have sucked in. Thus is it not probable that a cluster of matter would form around an evaporated black hole?
Moment of inertia in a ring is summationMR2. We can consider a spiral galaxy as a ring assuming it has lots of dark matter near its boundaries. Thus M and R will both be greater. Hence moment of inertia should increase, reducing speed of rotation. Thus it supports my counter-dark matter argument.

2. May 31, 2005

### SpaceTiger

Staff Emeritus
If you imagine a "ring" of matter in a circle around a galaxy's center, the energy (and therefore speed) of that ring's rotation will be determined by the mass interior to it. This comes from Newton's Law of Gravitation.

$$E=\frac{GM_{int}M_{ring}}{r}=\frac{1}{2}I_{ring}\omega^2=\frac{1}{2}M_{ring}^2r^2\omega^2$$

$$\omega=\sqrt{\frac{2GM_{int}}{r^3}}$$

Thus, more mass, faster rotation.

When black holes evaporate, they tend to emit radiation. Since this will escape the area around the black hole, there will be no cluster left in its wake.