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A-LEVEL 9702 · AS · TOPIC 3
Dynamics: the laws of motion
The chain of the topic: Newton's three laws give F = ma; momentum p = mv reframes the second law as F = Δp/Δt; resistive forces shape non-uniform motion up to terminal velocity; and because forces come in pairs, momentum is conserved in every collision. Around the hexagon are the three syllabus strands; above is what it builds on, below is where it leads.
TOPIC 3: DYNAMICS
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
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BUILDS ON
T1 Units & vectors of force T2 Kinematics: acceleration a 3.1
3.1
3.2
3.3
TOPIC 3
DYNAMICS
F = ma
1 · NEWTON'S LAWS & F = ma
Force is what changes a body's motion.
First law: with no resultant force, velocity stays constant.
Mass m is the resistance to a change in motion (inertia).
Second law: a is along the resultant force F.
Weight is gravity acting on mass.
F = m a W = m g
m
F
a
W = mg
a points the same way as the resultant force F
2 · MOMENTUM: THE DEEPER SECOND LAW
Force is the rate of change of momentum.
Linear momentum p = mv is a vector, in kg m s−¹.
F = Δp/Δt reduces to F = ma when m is constant.
Third law: the contact forces are equal and opposite.
A longer contact time means a smaller force for the same Δp.
F = Δp / Δt p = m v
A
B
F on B
F on A
third-law pair: equal in size, opposite in direction
3 · NON-UNIFORM MOTION
Resistive forces grow with speed.
Friction, viscous drag and air resistance oppose motion.
Falling: at first W > drag, so the body accelerates.
As v rises, drag rises until drag = weight.
Then the resultant force is zero, so a = 0: terminal velocity.
at terminal v: drag = mg, a = 0
t
v
terminal velocity
4 · CONSERVATION OF MOMENTUM
Total momentum is fixed with no external force.
For an isolated system: Σp before = Σp after.
Resolve and conserve momentum in 1D and 2D.
Elastic: kinetic energy is also conserved.
Inelastic: some kinetic energy becomes other forms.
elastic: speed of approach = speed of separation
u
before
v
after
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
LEADS TO
T4 Forces: equilibrium when ΣF = 0 T5 Energy: work done by a force F T12 Circular motion: F = ma toward the centre Each reuses F = ma: balanced forces give equilibrium, a force through a distance does work, and an inward force bends a path into a circle.
← Builds on IGCSE: Forces