Motion in a Circle · revision map · A-Level 9702, Topic 12

TOPIC 12 · MOTION IN A CIRCLE
CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 · ONE-PAGE REVISION MAP
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CIRCULAR MOTION12
Angular Quantities

Describe turning by angle, not distance. The radian is arc length per radius.

θ = s / r
1 turn = 2π rad = 360°

Angular speed ω is the angle swept per second. Every point of a rigid body shares the same ω.

ω = 2π / T = 2πf
unit rad/s
v = rω
links angular speed to
linear (tangential) speed
θ s v r arc s subtends angle θ at the centre; v stays tangent
Centripetal Acceleration & Force

At constant speed the velocity still keeps turning: a changing direction is an acceleration, directed to the centre.

By Newton's second law a net inward force must act.

a = v² / r = rω²
F = mv² / r = mrω²
a and F point toward the centre (centripetal)
v (tangent) a, F r velocity stays tangent; a and F aim to the centre
The Inward Force is Real

Something physical must supply the centripetal force F = mv²/r.

  • Tension, gravity, friction, the normal force or lift.
  • It is centre-seeking: always directed 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 if released
Solving & Applying

Choose the relation that fits the data given.

  • Given ω: use a = rω² and F = mrω².
  • Given v: use a = v²/r and F = mv²/r.
  • Bridges: v = rω,   T = 2π/ω.
  • On a banked track, the resultant of N and mg supplies the inward force mv²/r.
mg N mv²/r banked curve
BUILDS ON · Kinematics · Newton's laws → CIRCULAR MOTION → LEADS TO · Gravitational fields · Oscillations
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