LucidSTEM
A-LEVEL 9702 · A2 · TOPIC 12
Motion in a circle
The chain of the topic: the radian defines angle, angular speed follows, v = rω ties it to linear speed, and a constantly turning velocity demands a centripetal acceleration, and so a real inward force. Around the hexagon are the four ideas; above is what it builds on, below is where it leads.
TOPIC 12: MOTION IN A CIRCLE
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T1 Vectors T2 Kinematics T3 Newton's laws 12.1
12.2
12.2
use
TOPIC 12
CIRCULAR
MOTION
1 · ANGULAR QUANTITIES
Describe turning with angle, not distance.
The radian: θ = s / r one turn = 2π rad = 360°
Angular speed ω = Δθ / Δt = 2π / T = 2πf
Every point on a rigid body shares the same ω
v = r ω
links angular speed to linear speed
θ
s
r
v
arc s subtends angle θ at the centre
2 · CENTRIPETAL ACCELERATION & FORCE
Constant speed, but velocity keeps turning.
A changing direction is an acceleration, even at
steady speed, directed toward the centre.
By Newton's second law a net force acts inward.
a = v² / r = r ω²
F = m v² / r = m r ω²
v
a, F
r
v stays tangent; a and F point to the centre
3 · THE INWARD FORCE IS REAL
Something physical must supply F.
Tension, gravity, friction, the normal force, lift...
It is centripetal: ‘centre-seeking’, always inward.
Remove it and the body flies off in a straight line
(Newton's first law).
‘Centrifugal force’ is not a real force: it is inertia.
hand
T
flies off tangentially if released
4 · SOLVING & APPLYING
Choose the relation that fits the data.
Given ω: use a = rω² and F = m rω²
Given v: use a = v²/r and F = m v²/r
Bridges: v = rω, T = 2π/ω
On a banked track, the resultant of N and mg
supplies the inward force m v²/r.
mg
N
F = mv²/r
banked curve
LEADS TO
T13 Gravitational fields: orbits, GMm/r² = mv²/r T17 Oscillations: SHM as projected circular motion T20 Magnetic fields: charged particle, BQv = mv²/r Each reuses one idea: a real inward force equal to m v²/r bends a fast-moving body into a circle.
← Builds on IGCSE: Forces (circular motion)