00:01
The classical formula for momentum says p is equal to mv, which means that momentum is proportional or varies linearly with speed.
00:14
But the relativistic momentum says that the momentum is equal to gamma times mass time speed.
00:25
And gamma here is equal to 1 over 1 minus v.
00:30
V.
00:30
S squared over c square root over.
00:32
So momentum becomes equal to gamma times mass times velocity.
00:38
So now you can see that momentum and speed are not linearly related anymore.
00:47
And this means that the relativistic momentum increases with gamma or increases with speed but not linearly.
01:01
Now near v equal to c, gamma becomes close.
01:08
To infinity.
01:10
Therefore, you can say that momentum also tends to go to infinity.
01:18
So it is possible that if you increase 1%, if you increase the speed by 1%, the momentum increases by 5%.
01:29
Because near this value, when v tends to c or when the speed tends to the speed of sound, the momentum increases at a faster rate than speed.
01:42
So a 5 % increase in momentum for a 1 % increase in speed is quite possible.
01:47
Now let's prove this numerically.
01:53
So we will use this equation...