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4.1.2Linear Momentum

Rate of Change of Momentum — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 8 parts Lesson 3 of 13 1 quiz

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4.1.2 Rate of Change of Momentum — AP PHYSICS 1 notes: Express Newton's second law as net force equals rate of change of momentum and use it to find average forces.Fnet = Δp/Δt — the net external force equals the rate of change of momentum of an object or system.Fnet in N, Δp in …

  • Original form
  • Constant mass
  • Variable mass
  • Momentum–time graph
  • Definition
  • Stopping only

Section 1 of 8Newton's second law in momentum form

Fnet
Δp/Δt
  • the net external force equals the rate of change of momentum of an object or system.
  • Fnet in N, Δp in kg·m/s, Δt in s.
Original form
  • Newton's second law was originally postulated in terms of momentum.
Constant mass
  • Δp = mΔv, so Fnet = m(Δv/Δt) = ma.
Variable mass
  • Variable mass the momentum form still applies when the mass is not constant.

Section 2 of 8Interpreting the equation

Same Δp
  • Same Δp a large force for a short time or a small force for a long time gives the same change in momentum.
Direction
  • Direction the change in momentum points along the net force.
Momentum–time graph
  • Momentum–time graph a straight line with gradient Fnet for constant force; a curve means the force varies,
    • and the tangent gradient gives the force at that moment.

Section 3 of 8Calculating Δp

Definition
  • Δp = pf − pi = mvf − mvi, with signs.
Rebound
  • Rebound the velocity reverses sign, so |Δp| is nearly double the incoming momentum;
    • a ball rebounding at the same speed has Δp = −2mv.
Stopping only
  • Δp has magnitude mv, so a rebound needs a larger force for the same contact time.
Two dimensions
  • Two dimensions find Δp separately for x and y components.
Sign convention
  • Sign convention take the initial direction as positive unless told otherwise.

Section 4 of 8Variable mass: rain, jets and rockets

Variable mass: rain, jets and rockets
Rain or sand arriving with no horizontal velocity
  • Rain or sand arriving with no horizontal velocity needs a horizontal force F = v(Δm/Δt) even at steady speed.
Water jet on a wall
  • Water jet on a wall force equals the mass per second times the speed lost.
Rocket thrust
  • Rocket thrust equals the rate at which momentum is given to the exhaust gases.
System
  • System define the mass stopped or accelerated in Δt;
    • the forces on the water and on the wall are equal and opposite.

Section 5 of 8Why it matters

Why it matters
Safety devices
  • Safety devices air bags, crumple zones, padded dashboards and bent knees spread the same Δp over a longer Δt, reducing the average force.
Short contact
  • Short contact a hammer blow or karate chop uses a short time to create a large force.
Measurement
  • Measurement average force can be found from video analysis using Δp from the speeds and Δt from the frame times.
Systems
  • Systems internal forces cancel in pairs by Newton's third law, so the total momentum changes only through the net external force.

Section 6 of 8More from the specification

More from the specification
Momentum-time graph slope
  • Momentum-time graph slope the instantaneous tangent slope on a momentum-versus-time graph equates directly to the resultant external net force.
Inertia
  • Resistance of an object to changes in its motion.
Force-time graph
  • A graph whose area is the impulse.
Linear momentum
  • The product of mass and velocity.
Final velocity
  • Velocity at the end, v.
Kinetic energy
  • K = ½mv2, energy of motion.
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)
Collision
  • Short interaction with large internal forces.
Vector
  • Quantity with magnitude and direction.

Section 7 of 8Key terms

TermMeaning
Net forceVector sum of external forces, equal to Δp/Δt.
ΔpChange in momentum, final minus initial.
Average forceTotal change in momentum divided by the time interval.
Contact timeDuration over which two objects exert force on each other.
Crumple zoneCar structure that lengthens collision time and lowers force.

Section 8 of 8Exam technique

1
Forgetting that a rebound reverses the velocity, so Δp is larger than mv.
2
Using the final momentum instead of the change in momentum in F = Δp/Δt.
3
Ignoring signs — define a positive direction first.
4
Thinking larger momentum means larger force — it is the rate of change that matters.
5
Applying the equation to a single object when the force given is an internal force of the system.

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