# Why the mass of a particle increases as its speed increases

If a proton had a mass of 1.67 x 10-27kg at rest, what would its effective mass be if it was travelling at almost the speed of light (0.99c) with respect to an observer at rest?

Using the equation:

1.18 x 10-26kg is more than seven times 1.67 x 10-27kg

As the proton increases its speed its mass increases. At 0.99c the proton has an effective mass that is over 7 times greater than a proton at rest.

In the LHC, protons can achieve a velocity of 0.999999990c, or about 3.1ms-1 slower than the speed of light. At this speed the effective mass of the proton is 6930 times the rest mass. To the outside observer it would take 90μs to complete each 27km cycle, which equates to a frequency of 11,000 revolutions per second (hertz).

We can use relativity to show that in the proton’s frame of reference it would take 12.7ns to complete each cycle because the proton would measure the circumference to be only 3.8m.

From a stationary observer’s frame of reference the proton’s time will run much slower than the observer’s time. This is why the proton believes it takes such a short time.

From the proton’s frame of reference it gets around faster because it ‘sees’ the LHC moving near the speed of light and the circumference will contract in the direction of motion.