💥Impulse & Momentum
What is Momentum?
Linear momentum is the product of an object's mass and velocity:
p = mv
Momentum is a vector (same direction as velocity), measured in kg·m/s.
The more momentum an object has, the harder it is to stop. A slow-moving truck can have more momentum than a fast-moving bicycle.
Newton's Second Law can be written in terms of momentum: F = Δp/Δt
This is actually Newton's original formulation! "Net force equals rate of change of momentum."
Impulse
Impulse (J) is the change in momentum caused by a force acting over a time interval:
J = F · Δt = Δp = mv_f − mv_i
Impulse has units of N·s (= kg·m/s).
The Impulse-Momentum Theorem: J = Δp
This has important practical applications: - Airbags: increase collision time → reduce force needed to stop you - Bent knees: landing with bent knees increases time of impact, reducing peak force - Baseball swing: follow-through increases contact time, increases impulse on ball
Impulse Visualization
See how the same change in momentum can result from a large force for a short time, or a small force for a long time.
Think About It
A car crashes into a wall and stops. Would you rather it crash into a concrete wall or a padded barrier? Use impulse-momentum to explain why.
✏️ Worked Example
Problem: A 0.5 kg ball moving at 10 m/s is caught in 0.1 s. What average force does the catcher exert on the ball?
📐 Key Equations
Impulse and Momentum
p = mvJ = FΔ t = Δ pF = (Δ p)/(Δ t)⚠️ Common Mistakes
Misconception: Students confuse momentum with force — thinking a heavier or faster object "has more force."
✓ Correct thinking: Momentum (p = mv) is a property of the object's state of motion. Force is an interaction that changes momentum over time.
Why: Newton's Second Law: F = Δp/Δt. Force is the rate of change of momentum, not momentum itself.
Misconception: Forgetting that impulse and momentum are vectors — signs matter!
✓ Correct thinking: Always define a positive direction first. If the ball bounces back, its final velocity is negative relative to the initial direction.
Why: Δp = mv_f − mv_i. If the ball reverses direction, v_f is negative, making |Δp| larger than just stopping.
Misconception: Assuming a longer collision time means more impulse.
✓ Correct thinking: Longer collision time with the same force change gives the same impulse (Δp is fixed). Longer time just reduces the average force required.
Why: The change in momentum is determined by the initial and final velocities — the time only affects how large the average force is.
📝 Practice Problems
Try these problems. Check your answer when ready.
A 3 kg object is moving at 4 m/s. What is its momentum?
A 0.2 kg ball is thrown at 15 m/s and caught (brought to rest) in 0.05 s. What average force did the catcher exert on the ball?
A 1500 kg car traveling at 20 m/s brakes to a stop in 4 s. What is the average braking force?
A 0.5 kg ball hits a wall at 10 m/s and bounces back at 8 m/s (same axis). What is the impulse delivered to the ball?
A force of 200 N acts on a 4 kg object for 0.5 s, then an opposing force of 100 N acts for 1 s. If the object started at rest, what is its final velocity?
A 60 kg skateboarder rolling at 3 m/s pushes off a wall and rolls away at 5 m/s in the opposite direction. If the push lasted 0.2 s, what was the average force the wall exerted on the skateboarder?
F = (Δ p)/(Δ t)Finished reading through this lesson?