## Saturday, 28 April 2018

### Exercise 1.05 Particle accelerator

#### The question was

Particle physicists are so used to setting c=1 that they measure mass in units of energy. In particular, they tend to use electron volts (1 eV=1.6 x 10-12 erg=1.8 x 10-33 g), or, more commonly, keV, MeV, and GeV. The muon has been measured to have a mass of 0.106 GeV and a rest frame lifetime of 2.19 x 10-6 seconds. Imagine that such a muon is moving in the circular storage ring of a particle accelerator, 1 kilometer in diameter, such that the muon’s total energy is 1000 GeV. How long would it appear to live from the experimenter’s point of view? How many radians would it travel around the ring?

#### My answer was

First all I worked this out for  a (rather long) linear accelerator and converted to a circle. The muon will  whizz around it about 1,973 times, subtending an angle of 12,400 radians with a velocity of 0.999 999 99438c.

I was then less feeble and did it in polar coordinates using angular momentum.

On this occasion I completely agreed with Petra Axolotl, who did it in four lines.