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Theme A — Space, Time and Motion

A.2.16 Angular Velocity — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 27 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

A.2.16 Angular Velocity — IB PHYSICS SL notes: Describe circular motion using the radian, angular displacement, angular velocity, period and frequency, and relate angular and linear speed.Straight line — an object at constant velocity has zero acceleration and no resultant force.…

  • Uniform circular motion
  • If the string is cut
  • Arc length
  • Full circle
  • Degrees to radians
  • Radians to degrees

Part 1 of 8Straight line and circular motion

Straight line
  • Straight line an object at constant velocity has zero acceleration and no resultant force.
Circle
  • Circle a string attached to a puck pulls it at 90° to the velocity, so the direction changes but the speed does not.
Uniform circular motion
  • Uniform circular motion the speed is constant and the velocity changes direction, so the object accelerates.
If the string is cut
  • If the string is cut the puck moves off along the tangent in a straight line.

Part 2 of 8Radians

Radian
Radian the angle subtended at the centre of a circle by an arc equal in length to the radius.
Arc length
  • Arc length s = rθ.
Full circle
  • 2π rad = 360°, so 180° = π rad and 90° = π/2 rad.
Degrees to radians
  • Degrees to radians multiply by π/180.
Radians to degrees
  • Radians to degrees multiply by 180/π.
Dimensionless
  • Dimensionless radians have no unit in calculations.

Part 3 of 8Angular displacement and angular velocity

Angular displacement Δθ
Angular displacement Δθ the change in angle, in radians, of a body rotating around a circle.
  • Δθ = s/r, where s is the arc length.
Angular speed ω
Angular speed ω the rate of change of angular displacement, ω = Δθ/Δt.
  • It is a scalar with unit rad s−1.
Angular velocity
  • Angular velocity a vector with unit rad s−1, whose magnitude is the angular speed.
Constant ω
  • θ = ωt.
Whole body
  • Whole body all points of a rotating rigid body have the same ω, though linear speeds differ.
Independent of radius
  • ω does not depend on the length of the rotating line.

Part 4 of 8Period, frequency and linear speed

Period T
  • Period T the time for one revolution, in s.
Frequency f
  • Frequency f the number of revolutions per second, in Hz, with f = 1/T.
Angular speed
  • ω = 2π/T = 2πf, since one revolution is 2π rad.
    What the symbols mean: ω = angular frequency (rad s−1) · f = frequency (Hz) · T = period (s)
Linear speed
  • Linear speed v = ωr = 2πr/T, found from the circumference 2πr divided by T.
    What the symbols mean: v = speed (m s−1) · ω = angular speed (rad s−1) · r = radius (m) · T = period (s)
Direction of v
  • Direction of v the velocity is tangent to the circle, perpendicular to the radius.
Points farther out
  • Points farther out they move faster;
    • the Earth's equator moves at about 465 m s−1 while all points have ω = 7.3 × 10−5 rad s−1.

Part 5 of 8Using the equations

Units
  • Units angles must be in radians, so convert degrees first.
Revolutions per minute
  • Revolutions per minute multiply by 2π/60 to get rad s−1.
Typical values
  • Typical values clock second hand 0.105 rad s−1;
    • hour hand 1.45 × 10−4 rad s−1;
    • spin drum at 1200 rev per minute 126 rad s−1.
Wheel
  • Wheel at 25 m s−1 with radius 0.30 m, ω = 83 rad s−1.
Chain drive
  • Chain drive sprockets share the chain speed, so angular velocities are in inverse proportion to the radii.

Part 6 of 8Graph link

Horizontal position
  • Horizontal position plotted against time for a body in a circle, it is a sine or cosine wave of period T.
Link
  • Link this connects circular motion to simple harmonic motion.

Part 7 of 8Measuring ω

Stopwatch
  • Stopwatch count revolutions over a long time and divide, to reduce the timing uncertainty.
Light gate
  • Light gate use it with a marked rotating arm.

Part 8 of 8More from the specification

More from the specification
Centripetal Force in Circular Motion
  • An object undergoing uniform circular motion requires a net centripetal force directed toward the centre of the circle: Fc = mv² / r = mrω²,
  • where ω is angular velocity in rad s⁻¹.
Impulse and Change of Momentum
  • Linear impulse J is the product of average resultant force and time interval (J = FΔt),
  • which is mathematically equal to the change in momentum (Δp = mv - mu).
Conservation of Momentum in Collisions
  • In any closed system with no external resultant forces, total linear momentum is strictly conserved across elastic and inelastic collisions.
    • (Σ pinitial = Σ pfinal)
Fluid Resistance and Viscous Drag
  • Objects moving through fluids experience viscous drag;
    • according to Stokes' law for spherical particles of radius r, fluid resistance is Fd = 6πηrv,
  • leading to terminal fall speed.
Fluid resistance
  • Drag force from a fluid opposing motion.
Normal
  • Line at 90° to a surface.
Tension
  • Force transmitted along a string or rope.
Buoyancy
  • Another name for upthrust.
Centripetal force
  • Net force toward the centre, mv2/r.
Static friction
  • Friction between surfaces at rest relative to each other; fs ≤ μsFN.
Kinetic energy
  • K = ½mv2, energy of motion.
Centripetal acceleration
  • Ac = v2/r toward the centre.
Normal reaction
  • The contact force perpendicular to a surface.
Momentum
  • P = mv, a vector.
Friction
  • Force parallel to the surface opposing relative motion or its tendency.
Newton
  • Unit of force, kg m s-2.
Weight
  • Gravitational force on a mass.
Collision
  • Short interaction with large internal forces.
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)

Key terms

TermMeaning
RadianAngle subtended at the centre by an arc equal in length to the radius
Angular displacementChange in angle, in radians, of a body rotating around a circle
Angular velocityRate of change of angular displacement, ω = Δθ/Δt, in rad s−1
PeriodTime taken for one complete revolution
FrequencyNumber of revolutions per second, f = 1/T
Linear (tangential) speedSpeed along the circular path, v = ωr

Avoid these mistakes

1
Using degrees in v = ωr — angles must be in radians.
2
Thinking ω depends on the radius — v depends on r, ω does not.
3
Saying uniform circular motion has no acceleration — the velocity direction changes.
4
Using the period as the frequency — f = 1/T.
5
Forgetting to convert revolutions per minute — multiply by 2π/60.

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v = u + at  |  s = ut + ½at2  |  v2 = u2 + 2as  |  s = ½(u + v)t

  • Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
  • Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
  • Free Fall in vacuum: a = g ≈ 9.81 m/s2 downwards (air resistance negligible).
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