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9.1Momentum and Its Conservation

Impulse and Momentum — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 3 of 5 1 quiz

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Lesson summary

Define momentum and impulse and state their units.Momentum = mass × velocityp = mv (kg·m/s).Impulse = force × timeFΔt (N·s).Impulse = change in momentumFΔt = Δp = mvf − mvi.Resultant force = change in momentum ÷ time takenF = Δp/Δt (N).1 N·s = 1 kg·m/s.Area under a force–time gra…

  • Momentum is a vector
  • Newton's second law can be written F = Δp/Δt
  • Rearranging gives FΔt = Δp
  • Momentum and kinetic energy are different
  • Momentum (p)
  • Impulse–momentum theorem

Section 1 of 7Impulse and Momentum

Essential knowledge
9.1 Impulse and Momentum concept map: Momentum = mass × velocity, Impulse = force × time, Impulse = change in momentum, Resultant force = change in m, Momentum is a vector
Visual guide to the key ideas explained in this lesson.
Momentum measures how hard it is to stop a moving object; it depends on both mass and velocity. A slow truck and a fast bullet can have similar momentum.
Momentum is a vector
Momentum is a vector direction matters. In one dimension use + and − signs for opposite directions.
Newton's second law can be written F
Δp/Δt
the resultant force equals the rate of change of momentum. For constant mass this is the same as F = ma.
Rearranging gives FΔt = Δp
Rearranging gives FΔt = Δp the impulse of the force equals the change in momentum (impulse–momentum theorem).
Impulse can be increased either by a larger force or by applying it for longer – e.g. following through in golf or tennis increases contact time and so the ball's final momentum.
When stopping an object, Δp is fixed. Spreading the stop over a longer time reduces the average force; this is the principle of airbags, crumple zones, seat belts, padded gym floors and bending knees on landing.
On a force–time graph, the area under the curve is the impulse. For a varying force, the average force is the impulse divided by the time.
When an object bounces back, the change in momentum is larger than when it just stops, because the velocity changes sign: Δp = m(vf − vi) with opposite signs.
The unit N·s equals kg·m/s, showing impulse and momentum are the same kind of quantity.
Momentum and kinetic energy are different
Momentum and kinetic energy are different momentum is a vector (kg·m/s), KE is a scalar (J). Two objects can have equal momentum but different KE.

Section 2 of 7Process & sequence

1
Choose a positive direction and write it down.
2
Write initial and final velocities with signs (a rebound reverses sign).
3
Calculate initial momentum pi = mvi and final momentum pf = mvf.
4
Find the impulse Δp = pf − pi.
5
Divide by the contact time to find the average force F = Δp/Δt.
6
State magnitude, unit (N or N·s) and direction.

How an airbag reduces injurywrite these steps in this order; each step is a marking point.

1
In a crash the person's momentum must fall to zero – Δp is fixed.
2
The airbag lets the head decelerate over a longer time Δt.
3
Since F = Δp/Δt, a longer Δt means a smaller average force.
4
The force is also spread over a larger area, lowering pressure.
5
Smaller force and pressure mean less injury.

Section 3 of 7Compare

Safety features and impulse
FeatureWhat it changesEffect on force
AirbagIncreases stopping time of headSmaller average force
Seat belt (stretches slightly)Increases stopping time; spreads forceSmaller force and pressure
Crumple zoneIncreases collision timeSmaller force on occupants
Bending knees on landingIncreases time to stopSmaller force on legs
Helmet foamIncreases time head takes to stopSmaller force on skull

In each case Δp is fixed by the situation; only Δt can be changed.

Momentum vs kinetic energy
PropertyMomentumKinetic energy
Formulap = mvKE = ½mv2
Unitkg·m/sJ
Scalar/vectorVectorScalar
Conserved in all collisions (closed, isolated)?YesOnly in elastic collisions

Section 4 of 7Worked examples

−3.0 N·s
A 0.15 kg ball moving at 20 m/s is caught and stopped in 0.050 s. Find the impulse and the average force on the ball.
  • Take the ball's initial direction as +.
    Δp = m(vf − vi) = 0.15 × (0 − 20) = −3.0 N·s (3.0 N·s opposite to the motion)
    F = Δp/Δt = −3.0/0.050 = −60 N, i.e. 60 N opposite to the ball's motion.
825 N ≈ 830 N
A 0.060 kg tennis ball arrives at 25 m/s and leaves in the opposite direction at 30 m/s. Contact time 4.0 ms. Find the average force.
  • Take the leaving direction as +vi = −25 m/s, vf = +30 m/s.
    Δp = 0.060 × (30 − (−25)) = 0.060 × 55 = 3.3 N·s
    F = 3.3/0.0040 = 825 N ≈ 830 N in the direction the ball leaves.
A 1200 kg car speeds up from 10 m/s to 25 m/s. What impulse acted on it? If this took 6.0 s, what was the average resultant force?
  • Δp = 1200 × (25 − 10) = 1.8 × 104 N·s
    F = 1.8 × 104/6.0 = 3.0 × 103 N forwards.

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Momentum (p) · Impulse · Impulse–momentum theorem · Change in momentum (Δp) · Resultant (net) force · Newton's second law (momentum form) · Force–time graph · Average force · Crumple zone · Velocity (v) · Vector quantity
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
the airbag absorbs the momentumthe airbag increases the time taken to stop, so the rate of change of momentum (force) is smaller
2
momentum = mass × speedmomentum = mass × velocity (it is a vector)
3
impulse is a forceimpulse is force × time, equal to the change in momentum (N·s)
4
change in momentum = mv − mu without signschoose a positive direction; a rebound velocity is negative
5
force = change in momentumforce = change in momentum ÷ time taken

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