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4.2.1Linear Momentum

The Principle of Conservation of Momentum — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 10 parts Lesson 8 of 13 1 quiz

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4.2.1 The Principle of Conservation of Momentum — AP PHYSICS 1 notes: State the law of conservation of momentum, explain when it applies and use it in one dimension.Law — the total linear momentum of an isolated system remains constant unless acted on by a net external force: pi …

  • Vector sum
  • Impulses and changes
  • Only external forces
  • Two carts on a low-friction track
  • One cart only
  • Very short collisions

Section 1 of 10The principle

Law
  • Law the total linear momentum of an isolated system remains constant unless acted on by a net external force: pi = pf.
Vector sum
  • Vector sum m1vi1 + m2vi2 = m1vf1 + m2vf2.
Origin
  • Origin from Fnet = Δp/Δt: if Fnet,ext = 0 then Δp = 0.
Scope
  • Scope momentum, like energy, is conserved in all interactions.

Section 2 of 10Why internal forces cancel

Third law
  • Third law the forces between two objects are equal and opposite and act for the same time.
Impulses and changes
  • Impulses and changes equal and opposite impulses give Δp1 = −Δp2.
Only external forces
  • Only external forces forces from outside the system can change the total momentum.

Section 3 of 10Choosing the system

Choosing the system
Two carts on a low-friction track
  • Two carts on a low-friction track weights balance normal forces, so horizontal momentum is conserved.
One cart only
  • One cart only the other cart exerts an external force.
Very short collisions
  • Very short collisions friction and gravity have negligible impulse, so momentum is conserved just before and after.
One component only
  • One component only a projectile's horizontal momentum is constant while the vertical changes.
    • (no air resistance)

Section 4 of 10Examples of the law

Examples of the law
Identical objects approaching at equal speeds
  • Identical objects approaching at equal speeds momenta +mv and −mv cancel to a net momentum of zero.
Moving A hits stationary B and rebounds
  • Moving A hits stationary B and rebounds mAv0A = −mAvA + mBvB.
Trolleys 2m and m at equal speeds sticking
  • Trolleys 2m and m at equal speeds sticking they move off in the direction of the larger initial momentum.

Section 5 of 10Using the law

1
Define the system and verify that the net external force is zero in the direction considered.
2
Choose a positive direction and write the total initial momentum with signs.
3
Write the total final momentum.
4
Set the totals equal and solve.
Units
  • Units mass units can be anything if consistent on both sides; SI is safest.
Reference frame
  • Reference frame all velocities must be measured in the same frame.

Section 6 of 10Bar charts and graphs

Momentum bar chart
  • Momentum bar chart bars above the axis for positive momentum and below for negative;
    • the sum before equals the sum after.
Momentum–time graphs
  • Momentum–time graphs one object's momentum rises by the amount the other's falls;
    • total momentum is a horizontal line.

Section 7 of 10Justifying the use of the law

State
  • State the system explicitly.
Internal forces
  • Internal forces are equal and opposite.
External forces
  • External forces cancel or have negligible impulse over the short interaction.
    • (gravity, normal, friction)
Comparison with energy
  • Comparison with energy momentum is conserved in every isolated interaction, mechanical energy only in elastic ones.

Section 8 of 10More from the specification

Explosion
  • Interaction pushing parts of a system apart.
Kinetic energy
  • K = ½mv2, energy of motion.
Inelastic collision
  • Momentum conserved, kinetic energy not.

Section 9 of 10Key terms

TermMeaning
Isolated systemSystem with zero net external force.
External forceForce exerted by an object outside the system.
Internal forceForce between objects within the system.
Conservation of momentumTotal momentum constant when no net external force acts.
RecoilBackward motion of an object as it launches another.

Section 10 of 10Exam technique

1
Applying conservation of momentum when a significant external force such as friction acts.
2
Forgetting signs of velocities in opposite directions.
3
Thinking each object's momentum is conserved — only the total is.
4
Confusing conservation of momentum with conservation of kinetic energy.
5
Using the common speed for only one object when they stick.

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