MECHANICS:
centripetal force:
A particle with mass m will move on a circle line (radius r) if the direction of the (resulting) force F on the particle is perpendicular to the velocity vector of the particle.
MAGNETISM:
Lorentz force:
A charged particle (charge q) that is moving with velocity v perpendicular to a magnetic field of strength B will fell a force, the Lorentz force, perpendicular to both the field and the direction of motion.
SPECIAL RELATIVITY:
Lorentz contraction:
gamma factor:
c: velocity of light
Consider a body resting in an inertial system K. In this system the body has length l. In point of view from a inertial system K`, which is moving with the velocity v relatively to K, the length l' of the body is shorter. This is the Lorentz contraction.
Time dilatation: t = g t'
Energy-momentum relation: 
where m is the rest (invariant) mass of a particle.