Lesson 3 of 11 · 11 min
Newton's second law, momentum and impulse
NCERT § "Newton's Second Law of Motion"
In the outfield a 0.15 kg ball comes at Rohan at 20 m/s. He can meet it with stiff palms or let his hands ride back with it. It stops either way. Why does one of them sting?
The lesson in notes
In short
Linear momentum is p = mv, a vector along the velocity. Its SI unit is kg m s⁻¹.
The second law: the net external force on a body equals the time rate of change of its momentum, F = dp/dt, and the momentum changes in the direction of that force. For constant mass this gives F = ma.
The SI unit of force is the newton: 1 N = 1 kg m s⁻².
The law is a vector equation and can be applied component by component; a force perpendicular to the velocity changes the direction of motion but not the speed.
Acceleration at an instant depends on the force at that instant, not on the history of motion. A stone dropped from a moving train has, just after release, only the gravitational acceleration.
Impulse is force multiplied by time for a force acting briefly, and it equals the change in momentum: J = FΔt = Δp. Its unit is N s, the same as momentum.
The same change in momentum over a longer time needs a smaller average force; this is why a fielder draws the hands back while catching a fast ball.
For a ball that rebounds, the change in velocity is the sum of the two speeds, because the direction reverses.