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Theme A — Space, Time and Motion

A.2.3 Newton’s Second Law — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 14 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين نيوتن للحركة - Newton Laws of Motion FormulasFast Exam Solution
F = m × a | W = m × g | F₁₂ = -F₂₁
Word Equation & Conditions: القوة المحصلة = الكتلة × التسارع | Force = Mass × Acceleration
Location & Specifications: الميكانيكا الكلاسيكية والتحصيلي وفيزياء 3 ثانوي و IGCSE Physics.
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Lesson summary

A.2.3 Newton’s Second Law — IB PHYSICS SL notes: State and use F = ma and the momentum form of the second law to find accelerations, forces and masses.Newton's second law — the resultant force on a body is directly proportional to its acceleration and equals the rate of change of…

  • Constant mass
  • What the symbols mean
  • The newton
  • Proportionality
  • Only the resultant counts
  • Weight and mass

Part 1 of 7The law

Newton's second law
  • Newton's second law the resultant force on a body is directly proportional to its acceleration and equals the rate of change of its momentum.
Constant mass
  • F = ma.
    What the symbols mean: F = resultant force (N) · m = mass (kg) · a = acceleration (m s−2)
  • F is the resultant force in N, m the mass in kg and a the acceleration in m s−2.
The newton
  • 1 N is the force that gives a 1 kg mass an acceleration of 1 m s−2, so 1 N = 1 kg m s−2.
Direction
  • Direction the acceleration is always in the same direction as the resultant force.

Part 2 of 7What the equation shows

1Proportionality
  • Proportionality a is directly proportional to F and inversely proportional to m.
  • Doubling the force doubles the acceleration and doubling the mass halves it.
2Only the resultant counts
  • Only the resultant counts large forces that balance give zero acceleration.
3Weight and mass
  • Weight and mass mass is the amount of matter (kg, scalar) and weight is the gravitational force W = mg (N, vector).
4Free fall
  • Free fall mg = ma gives a = g for all masses when drag is absent.

Part 3 of 7Effects of the resultant force

Effects of the resultant force
Along the motion
  • Along the motion the body speeds up or slows down.
At an angle to the motion
  • At an angle to the motion the body changes direction.
Opposing the motion
  • Opposing the motion the body decelerates; it does not suddenly travel backwards.
Resultant at an angle
  • Resultant at an angle find it by combining vectors or by scale drawing.
Sign convention
  • Sign convention take the direction of initial motion as positive, so drag forces are negative.

Part 4 of 7Momentum form

Momentum form
Rate of change of momentum
  • F = Δp/Δt, with the change in momentum in the direction of the force.
Derivation
  • Derivation p = mv, so Δp/Δt = mΔv/Δt = ma for constant mass.
    What the symbols mean: p = momentum (kg m s−1) · m = mass (kg) · v = velocity (m s−1)
Variable mass
  • Variable mass the momentum form covers a rocket or a conveyor belt loading sand.
Force–time graph
  • Force–time graph the area under it is the change in momentum.
Limit
  • Limit the law applies in inertial frames and gives way to relativistic mechanics near the speed of light.

Part 5 of 7Connected bodies and slopes

Connected bodies and slopes
Connected bodies
  • Connected bodies apply the law to each body separately or to the whole system.
  • The resultant external force on a pair is (m1 + m2)a.
  • The tension is found by applying F = ma to one body.
Slope
  • Slope the resultant is mg sin θ down the slope minus friction.
Lift accelerating upwards
  • Lift accelerating upwards the cable tension is T = m(g + a), larger than the weight.

Part 6 of 7Strategy for dynamics problems

1
Draw a free-body diagram.
2
Take the direction of acceleration as positive.
3
Write the resultant force along it as a signed sum.
4
Equate the sum to ma, using one equation per body for connected bodies.
5
Use SI units: convert g to kg and kN to N.
6
Check limits: an acceleration above g for a freely hanging mass or a negative tension signals an error.

Part 7 of 7More from the specification

1Centripetal acceleration in circular motion
  • Centripetal acceleration in circular motion objects moving in a circle at constant speed experience centripetal acceleration whose magnitude depends on angular velocity.
2Rate of change of momentum
  • Rate of change of momentum the resultant force acting on an accelerated object equals its change in linear momentum divided by contact time.
3Fluid resistance and terminal speed
  • Fluid resistance and terminal speed opposing fluid drag increases with velocity until balancing the applied driving force, maintaining steady terminal motion.
4Newton's Second Law of Motion
  • The resultant net force acting on an object is equal to its rate of change of linear momentum, pointing in the direction of acceleration.
    • (F = Delta p / Delta t = m * a)
5Motion in a Horizontal Circle
  • An object traveling at constant speed in a circular path undergoes uniform circular motion with changing velocity direction, requiring a centripetal force of magnitude F = m * v2 / r = m * omega2 * r directed toward the center.
6Drag Forces in a Fluid
  • When an object moves through a fluid, viscous resistive forces act in opposition to velocity,
  • increasing with speed until net resultant force becomes zero at terminal velocity.
7Impact Forces During a Collision
  • In a collision between objects, the magnitude of impact force experienced is inversely proportional to collision duration, illustrating why extending impact time mitigates peak collision forces.
    • (F = m * Delta v / Delta t)
8Fluid resistance
  • Drag force from a fluid opposing motion.
9Normal
  • Line at 90° to a surface.
10Buoyancy
  • Another name for upthrust.
11Centripetal force
  • Net force toward the centre, mv2/r.
12Static friction
  • Friction between surfaces at rest relative to each other; fs ≤ μsFN.
13Kinetic energy
  • K = ½mv2, energy of motion.
14Angular speed
  • Magnitude of the angular velocity.
15Centripetal acceleration
  • Ac = v2/r toward the centre.
16Normal reaction
  • The contact force perpendicular to a surface.
17Collision
  • Short interaction with large internal forces.
18Linear
  • A graph that is a straight line through the origin, so resistance is constant.
19Impulse
  • J = FΔt = Δp.
20Radius
  • Distance from the centre to the circular path.

Key terms

TermMeaning
Newton's second lawResultant force equals the rate of change of momentum, F = ma for constant mass
Newton (N)Force that gives a 1 kg mass an acceleration of 1 m s−2
Resultant forceVector sum of all forces acting on a body
MassAmount of matter in a body and a measure of its inertia
WeightGravitational force on a body, W = mg
MomentumProduct of mass and velocity, p = mv

Avoid these mistakes

1
Using an individual force instead of the resultant in F = ma — use the resultant.
2
Leaving out the mass of all bodies that accelerate together — include the whole system.
3
Mixing up mass and weight, or using kg as a unit of force — weight is in N.
4
Taking tension equal to the hanging weight when the system accelerates — apply F = ma.
5
Thinking acceleration follows the velocity — it follows the resultant force.

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