9.1.1

Circular Motion

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Radians

A radian is another unit for measuring angles. There are 2π2\pi radians in a full circle. The radian unit can be written as rad.

Definition of a radian

Definition of a radian

  • The angle between two radii of a circle connected by an arc length that is equal in length to the radius is equal to one radian.
Comparison to degrees

Comparison to degrees

  • There are 2π\pi radians and 360 degrees in a circle.
  • If an object travels all the way around a circle it has done one revolution.
    • 1 rad=3602π≈57.3o1\text{ rad}=\frac{360}{2\pi} \approx 57.3^o
Change in angle

Change in angle

  • For a circle of radius rr, the change in angle is equal to the distance moved along the circumference divided by the radius.
  • The distance along the circumference moved is Δs\Delta s.
  • This can be written as Δθ=Δsr\Delta\theta = \frac{\Delta s}{r}

Angular Speed

Angular speed measures how quickly an object is rotating. The units of angular speed are radians per second (rad s-1).

Calculating angular velocity

Calculating angular velocity

  • Angular velocity is the change in angle of an object over a period of time. The equation for calculating angular velocity is:
    • Angular velocity = change in angle ÷ change in time
    • ω=Δθ/Δt\omega = {\Delta\theta} / {\Delta}t
Comparison to linear velocity

Comparison to linear velocity

  • Linear velocity is when an object is travelling in a straight line:
    • v=Δs/Δtv={\Delta}s/{\Delta}t
  • The radian equation helps us compare linear and angular velocity:
    • Δs=rΔθ{\Delta}s=r{\Delta\theta}
  • By substituting one into the other, we get the following equation:
    • v=rωv=r{\omega}
  • From this equation, we know that linear velocity is proportional to the distance from the centre, r.

Period of Circular Motion

In circular motion, the period and frequency are linked to the angular speed. These are helpful quantities to know if we need to calculate the angular speed.

Period and frequency

Period and frequency

  • In circular motion, the period of an object is how long it takes to travel all the way around the circle.
  • In circular motion, the frequency of an object is how many times it goes around the circle in one second.
    • Period = 1 ÷ frequency of the object
    • T=1  ÷  fT=1\;{\div}\;f
Calculating angular speed

Calculating angular speed

  • The equation for calculating angular speed is:
    • Angular velocity = 2 × pi × frequency of the object
    • ω=2π  ×  f{\omega}=2{\pi}\; {\times}\; f
  • By using T=1  ÷  fT=1\;{\div}\;f, we get:
    • ω=2π  ÷  T{\omega}=2{\pi}\;{\div}\;T
Jump to other topics
1

Physical Quantities & Units

1.1

Physical Quantities & Units

1.1.1Use of SI Units1.1.2SI Prefixes, Standard Form & Converting Units1.1.3End of Topic Test - Units & Prefixes1.1.4Avogadro's Constant1.1.5Scalars & Vectors
1.2

Errors & Uncertainty

1.2.1Measuring Length, Time & Volume1.2.2Measuring Temperature1.2.3Circuit Measurements1.2.4Limitation of Physical Measurements1.2.5Uncertainty1.2.6Estimation1.2.7Displaying Data1.2.8End of Topic Test - Measurements & Errors
2

Kinematics

2.1

Equations of Motion

2.1.1Motion in a Straight Line2.1.2Graphs of Motion2.1.3Bouncing Ball Example2.1.4End of Topic Test - Motion in a Straight Line2.1.5Acceleration Due to Gravity
3

Dynamics

3.1

Momentum & Newton's Laws of Motion

3.1.1Mass & Inertia3.1.2Newton's Laws3.1.3Momentum3.1.4End of Topic Test - Newton's Laws & Momentum3.1.5A-A* (AO3/4) - Newton's Third Law
3.2

Non-Uniform Motion

3.2.1Projectile Motion
3.3

Linear Momentum & Conservation

3.3.1Conservation of Momentum
4

Force, Density & Pressure

4.1

Force, Density & Pressure

4.1.1Fields4.1.2Force in Uniform Fields4.1.3Friction4.1.4Buoyancy4.1.5Terminal Speed4.1.6End of Topic Test - Acceleration Due to Gravity4.1.7Centre of Mass4.1.8Forces & Equilibrium4.1.9End of Topic Test - Scalars & Vectors4.1.10Moments4.1.11End of Topic Test - Moments & Centre of Mass4.1.12Density4.1.13Pressure
5

Work, Energy & Power

5.1

Work, Energy & Power

5.1.1Work & Energy5.1.2Power & Efficiency5.1.3Conservation of Energy5.1.4End of Topic Test - Work, Energy & Power
5.2

Gravitational Fields

5.2.1Newton's Law5.2.2Gravitational Field Strength5.2.3Gravitational Potential
6

Deformation of Solids

6.1

Materials

6.1.1Bulk Properties of Solids6.1.2Energy in Materials6.1.3Young Modulus6.1.4End of Topic Test - Materials
7

Waves

7.1

Simple Harmonic Motion

7.1.1Simple Harmonic Motion7.1.2Simple Harmonic Systems7.1.3Energy in Simple Harmonic Motion7.1.4Resonance7.1.5End of Topic Test - Simple Harmonic Motion7.1.6A-A* (AO3/4) - Simple Harmonic Motion7.1.7End of Topic Test - Gravitational Fields
7.2

Waves

7.2.1Progressive Waves7.2.2Intensity of Waves7.2.3Wave Speed & Phase Difference7.2.4Longitudinal & Transverse Waves7.2.5End of Topic Test - Progressive Waves7.2.6Electromagnetic Waves7.2.7Doppler Effect7.2.8Sound Waves7.2.9Measuring Sound Waves7.2.10End of Topic Test - Waves7.2.11Ultrasound Imaging7.2.12Ultrasound Imaging 2
8

Superposition

8.1

Superposition

8.1.1Stationary Waves8.1.2Stationary Waves 28.1.3End of Topic Test - Stationary Waves8.1.4A-A* (AO3/4) - Stationary Waves8.1.5Interference8.1.6Interference 28.1.7End of Topic Test - Interference8.1.8Diffraction8.1.9Diffraction Gratings8.1.10End of Topic Test - Diffraction
9

Thermal Physics

9.1

Circular Motion

9.1.1Circular Motion9.1.2Circular Motion 29.1.3End of Topic Test - Circular Motion
9.2

Thermal Physics

9.2.1Temperature9.2.2Measuring Temperature9.2.3Ideal Gas Law9.2.4Ideal Gases9.2.5Boyle's Law & Charles' Law9.2.6Molecular Kinetic Theory Model9.2.7Molecular Kinetic Theory Model 29.2.8Thermal Energy Transfer9.2.9Thermal Energy Transfer Experiments9.2.10End of Topic Test - Thermal Energy & Ideal Gases9.2.11First Law of Thermodynamics
10

Communication

10.1

Communication Channels

10.1.1Communication Channels10.1.2Modulation10.1.3Attenuation
10.2

Digital Communication

10.2.1Digital & Analogue Signals10.2.2Representing Sound
11

Electric Fields

11.1

Electric Fields

11.1.1Coulomb's Law11.1.2Electric Field Strength11.1.3Electric Field Strength 211.1.4Electric Potential11.1.5End of Topic Test - Electric Fields11.1.6A-A* (AO3/4) - Electric and Gravitational Field
11.2

Capacitance

11.2.1Capacitance11.2.2Parallel Plate Capacitor11.2.3Energy Stored by a Capacitor11.2.4Capacitor Discharge11.2.5Capacitor Charge
12

Current Electricity

12.1

Current Electricity

12.1.1Basics of Electricity12.1.2Mean Drift Velocity12.1.3Current-Voltage Characteristics12.1.4End of Topic Test - Basics of Electricity12.1.5Resistivity12.1.6End of Topic Test - Resistivity & Superconductors12.1.7Power and Conservation12.1.8Microphones12.1.9Components12.1.10Relays12.1.11Strain Gauges
12.2

DC Circuits

12.2.1Circuits12.2.2Potential Divider12.2.3Emf & Internal Resistance12.2.4End of Topic Test - Power & Potential
13

Magnetic Fields

13.1

Magnetic Fields

13.1.1Magnetic Flux Density13.1.2End of Topic Test - Capacitance & Flux Density13.1.3Moving Charges in a Magnetic Field13.1.4Magnetic Flux & Flux Linkage13.1.5Electromagnetic Induction13.1.6Electromagnetic Induction 213.1.7Magnetic Flux Density13.1.8Magnetic Resonance Scanning
13.2

Alternating Currents

13.2.1Alternating Currents13.2.2Operation of a Transformer13.2.3End of Topic Test - Electromagnetic Induction & AC13.2.4Rectification
14

Modern Physics

14.1

Quantum Physics

14.1.1The Photoelectric Effect14.1.2The Photoelectric Effect Explanation14.1.3End of Topic Test - The Photoelectric Effect14.1.4Collisions of Electrons with Atoms14.1.5Energy Levels & Photon Emission14.1.6Wave-Particle Duality14.1.7End of Topic Test - Absorption & Emission14.1.8Band Theory14.1.9Diagnostic X-Rays14.1.10X-Ray Image Processing14.1.11Absorption of X-Rays14.1.12CT Scanners
14.2

Nuclear Physics

14.2.1Rutherford Scattering14.2.2Atomic Model14.2.3Isotopes14.2.4Stable & Unstable Nuclei14.2.5A-A* (AO3/4) - Stable & Unstable Nuclei14.2.6Alpha & Beta Radiation14.2.7Gamma Radiation14.2.8Particles, Antiparticles & Photons14.2.9Quarks & Antiquarks14.2.10Particle Interactions14.2.11Radioactive Decay14.2.12Half Life14.2.13End of Topic Test - Radioactivity14.2.14Nuclear Instability14.2.15Mass & Energy14.2.16Binding Energy14.2.17A-A* (AO3/4) - Nuclear Fusion

Practice questions on Circular Motion

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    How many radians make a full turn?Multiple choice
  2. 2
    What is π radians in degrees?Multiple choice
  3. 3
    What is the correct equation for angular speed?Multiple choice
  4. 4
    How does the linear velocity of an object relate to the angular velocity?Multiple choice
  5. 5
    What is the period of an object moving around a circle?Multiple choice
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End of Topic Test - Diffraction

Circular Motion 2