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4.1Linear Momentum

Linear Momentum — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 10 parts Lesson 2 of 13 1 quiz

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Lesson summary

4.1 Linear Momentum — AP PHYSICS 1 notes: Describe the linear momentum of an object or system and relate it to velocity of the centre of mass and kinetic energy.p = mv — momentum is the product of mass and velocity, in kg·m/s (equivalent to N·s).Vector — it has the direction of t…

  • Direction change
  • Same momentum
  • Total momentum
  • Opposite motions
  • Velocity of centre of mass
  • Fnet = Δp/Δt

Section 1 of 10Linear momentum

p = mv
What the symbols mean: p = momentum (kg m s−1) · m = mass (kg) · v = velocity (m s−1)
  • momentum is the product of mass and velocity, in kg·m/s.
    • (equivalent to N·s)
Vector
  • Vector it has the direction of the velocity, so a sign convention is needed in one dimension.
At rest
  • At rest an object with v = 0 has zero momentum.
Direction change
  • Direction change changing direction alone changes momentum even if speed and kinetic energy stay the same.

Section 2 of 10Momentum and inertia

Momentum
  • Momentum shows how difficult it is to stop the motion; it changes with mass or velocity.
Inertia
  • Inertia shows how difficult it is to accelerate from rest; it changes only with mass.
Same momentum
  • Same momentum a 60 g ball at 75 m/s and a 3 kg brick at 1.5 m/s both have 4.5 kg·m/s, but the brick has greater inertia.

Section 3 of 10Momentum of a system

Momentum of a system
Total momentum
  • Total momentum psys = Σmivi, the vector sum.
Opposite motions
  • Opposite motions total momentum can be zero while each object has momentum, but system kinetic energy is zero only if all are at rest.
Centre of mass
  • Centre of mass xcm = Σmixi/Σmi.
Velocity of centre of mass
  • Velocity of centre of mass vcm = Σmivi/Σmi = ptotal/Mtotal.

Section 4 of 10Momentum and kinetic energy

FeatureMomentumKinetic energy
Formulap = mvK = ½mv2
TypeVectorScalar
SignCan be negativeNever negative
In collisionsConserved if isolatedConserved only if elastic
  • Relation
    • K = p2/(2m); with equal momentum the lighter object has more kinetic energy.

Section 5 of 10Newton's second law in momentum form

  • Fnet = Δp/Δt
    • the net external force equals the rate of change of momentum, giving F = ma for constant mass.

Section 6 of 10Collision and explosion models

Collision
  • Collision an interaction in which forces between the objects are much larger than the net external force.
Object model
  • Object model only initial and final states are analysed.
Explosion
  • Explosion an interaction in which internal forces move objects within the system apart.

Section 7 of 10Finding the total momentum

1
Choose a positive direction.
2
List the mass and signed velocity of every object.
3
Calculate p = mv for each.
4
Add the momenta as vectors, keeping signs.
5
Divide total momentum by total mass to find vcm if required.

Section 8 of 10More from the specification

More from the specification
Automotive deceleration in crumple zones
  • Automotive deceleration in crumple zones progressive structural collapse of crumple zones mitigates impact momentum of vehicles descending a highway slope.
Average force
  • F = Δp/Δt.
Force-time graph
  • A graph whose area is the impulse.
Crumple zone
  • Car structure that lengthens collision time and lowers force.
Impulse
  • J = FΔt = Δp.
    What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)

Section 9 of 10Key terms

TermMeaning
Momentump = mv, a vector.
System momentumVector sum of individual momenta.
Centre of massMass-weighted average position.
Velocity of centre of massTotal momentum divided by total mass.
CollisionShort interaction with large internal forces.
ExplosionInteraction pushing parts of a system apart.

Section 10 of 10Exam technique

1
Treating momentum as a scalar.
2
Forgetting signs when adding momenta.
3
Assuming equal momenta mean equal kinetic energies.
4
Confusing momentum with inertia.

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