Momentum & Impulse

Before we even touch impulse, let's be crystal clear on momentum. Momentum (symbol p) is a measure of "how hard it would be to stop something." A heavy truck moving slowly and a small car moving fast might have similar momentum — both would be a pain to stop suddenly.

Momentum is measured in kg m s⁻¹, and — critically — it's a vector. That means direction matters. If you take "moving right" as positive, then something moving left has negative momentum. This single fact trips up more students than anything else in this chapter, so keep it front of mind.

Newton's second law, in its most general form, isn't actually F = ma — it's this:

Think about it this way: if you're catching a fast cricket ball, the ball's momentum has to drop to zero. That change in momentum, Δp, is fixed — it depends only on the ball's mass and speed. But how you bring it to zero is up to you. If you snatch it rigidly, Δt is tiny, so F must be huge (it stings!). If you let your hands "give" and move backward with the ball, you stretch out Δt, which means F is much smaller. Same Δp, different force, because you changed the time.

Rearranging that force equation gives us the definition of impulse — the effect a force has when it acts for a certain amount of time.

the same unit

a small force acting for a long time has exactly the same effect as a large force acting for a short time

• increase reduces

vector