Why do particles moving in circular motion emit em radiation? For example particles moving in a synchrotron . Which energy of the particle is converted to the energy of the radiation ? What is the relation between this energy and the change in direction of the particle?. 
Thankyou for the help .
 A: Kinetic energy and photon absorption
Particles - when moving into a magnetic field - have gained before kinetic energy. As GRB wrote:

Every time a charged particle has to be accelerated, a photon has to be involved. If you want to linearly accelerate a charged particle, you have to shoot photons at its back.

To be precise this one of the possibilities of accelerating electrons, the second is the acceleration between a electric potential difference. It seems to be natural that electrons in the case of de-acceleration (braking) will re-emit photons. In other words, electrons have the possibility to absorb and to emit photons, the first happens in accelerations the second during braking.
Intrinsic spin, magnetic dipole moment and gyroscopic effect
The electron has a permanent magnetic dipole moment and an aligned with it intrinsic spin. As we know from Stern-Gerlach-experiment the spin has indeed to do with a momentum.
A electron at rest in a magnetic field will be aligned. Not spectacular. A moving electron in a magnetic field will be aligned too. But this time the straight line of the trajectory over goes to a spiral path which in reality is a path of tangerine slices. What happens?
The alignment of the electrons magnetic dipole moment lead to the deflection of the moving electron and this acceleration (every (non-gravitational) movement in circles is an acceleration) lead to the emission of photons. The photon has a momentum and this disaligne the electrons magnetic dipole moment again (gyroscopic effect). This process runs in cycles until the electron comes to rest.
I apologise for my bad English.
