Circular Motion

Radians

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

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

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

Change in angle

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

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

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
- $\omega = {\Delta\theta} / {\Delta}t$

Comparison to linear velocity

Linear velocity is when an object is travelling in a straight line:
- $v={\Delta}s/{\Delta}t$
The radian equation helps us compare linear and angular velocity:
- ${\Delta}s=r{\Delta\theta}$
By substituting one into the other, we get the following equation:
- $v=r{\omega}$
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

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
- $T=1\;{\div}\;f$

Calculating angular speed

The equation for calculating angular speed is:
- Angular velocity = 2 × pi × frequency of the object
- ${\omega}=2{\pi}\; {\times}\; f$
By using $T=1\;{\div}\;f$ , we get:
- ${\omega}=2{\pi}\;{\div}\;T$

1Space, Time & Motion

1.1Motion

1.1.1Motion Basics

1.1.2Graphs of Motion

1.1.3Uniform Acceleration Equations

1.1.4Projectile Motion

1.1.5Bouncing Ball Example

1.2Forces

1.2.1Friction

1.2.2Terminal Speed

1.2.3Newton's Laws

1.2.4Exam-Style Question - Forces

1.2.5End of Topic Test - Newton's Third Law

1.3Momentum & Impulse

1.3.1Momentum

1.3.2Momentum 2

1.3.3End of Topic Test - Newton's Laws & Momentum

1.4Work, Energy & Power

1.4.1Work & Energy

1.4.2Conservation of Energy

1.4.3Power & Efficiency

1.4.4IB Multiple Choice- Work, Energy & Power

2The Particulate Nature of Matter

2.1Thermal Concepts

2.1.1Molecular Kinetic Theory Model

2.1.2Molecular Kinetic Theory Model 2

2.1.3Thermal Energy Transfer

2.1.4Thermal Energy Transfer Experiments

2.1.5Thermal Equilibrium

2.1.6Thermal Conductivity

2.1.7Heat Energy Transfer

2.2Modelling a Gas

2.2.1Ideal Gases

2.2.2Ideal Gases 2

2.2.3End of Topic Test - Thermal Energy & Ideal Gases

2.2.4Exam-Style Question - Ideal Gases

3Wave Behaviour

3.1Oscillations

3.1.1Progressive Waves

3.1.2Simple Harmonic Motion

3.2Travelling Waves

3.2.1Wave Speed & Phase Difference

3.2.2Longitudinal & Transverse Waves

3.2.3Electromagnetic Waves

3.2.4Electromagnetic Waves 2

3.2.5Sound Waves

3.3Wave Characteristics

3.3.1Polarisation

3.4Wave Behaviour

3.4.1Reflection & Absorption

3.4.2Reflection of Light

3.4.3Refraction

3.4.4Refractive index

3.5Standing Waves

3.5.1Standing Waves

3.5.2Standing Waves 2

3.5.3End of Topic Test - Standing Waves

3.5.4IB Multiple Choice - Waves

3.6Simple Harmonic Motion

3.6.1Simple Harmonic Motion

3.6.2Simple Harmonic Systems

3.6.3Energy in Simple Harmonic Motion

3.6.4End of Topic Test - Simple Harmonic Motion

3.6.5End of Topic Test - Simple Harmonic Motion

3.7Single Slit Diffraction

3.7.1Diffraction

3.8Interference

3.8.1Interference

3.8.2Interference 2

3.8.3Diffraction Gratings

3.8.4End of Topic Test - Diffraction

3.9Doppler Effect

3.9.1Doppler Effect

4Fields

4.1Circular Motion

4.1.1Circular Motion

4.1.2Centripetal Force

4.1.3IB Multiple Choice - Circular Motion

4.2Newton's Law of Gravitation

4.2.1Newton's Law

4.2.2Orbits of Planets & Satellites

4.2.3Escape Velocity & Synchronous Orbits

4.2.4End of Topic Test - Gravitational Fields

4.3Fields

4.3.1Fields

4.3.2Gravitational Field Strength

4.3.3Gravitational Potential

4.3.4Electric Field Strength

4.3.5Electrostatic & Gravitational Forces

4.3.6Electric Potential

4.3.7IB Multiple Choice - Gravitational Fields

4.4Fields at Work

4.4.1Radial Field Strength

4.4.2Orbits of Planets & Satellites

4.4.3Escape Velocity & Synchronous Orbits

4.4.4End of Topic Test - Gravitational Fields

4.4.5Uniform Electric Fields

4.4.6IB Multiple Choice - Electric Field & Potential

4.5Electric Fields

4.5.1Electric Charge

4.5.2Conservation of Charge

4.5.3Coulomb's Law

4.5.4Current

4.5.5Potential Difference

4.5.6IB Multiple Choice - Electric Charge

4.6Magnetic Effect of Electric Currents

4.6.1Magnetism

4.6.2Magnetic Field

4.6.3Magnetic Force

4.6.4Moving Charges in a Magnetic Field

4.6.5IB Multiple Choice - Magnetism

4.7Heating Effect of Currents

4.7.1Circuits

4.7.2Resistance

4.7.3Power and Conservation

4.7.4IB Multiple Choice - DC Circuits

4.8Electromagnetic Induction

4.8.1Electromagnetic Induction

4.8.2Electromagnetic Induction 2

4.8.3Magnetic Flux & Flux Linkage

4.8.4End of Topic Test - Electromagnetic Induction

4.9Power Generation & Transmission

4.9.1Alternating Currents

4.9.2Operation of a Transformer

4.10Capacitance

4.10.1Capacitance

4.10.2Parallel Plate Capacitor

4.10.3Energy Stored by a Capacitor

4.10.4Capacitor Discharge

4.10.5Capacitor Charge

4.10.6Magnetic Flux Density

4.10.7End of Topic Test - Capacitance & Flux Density

5Nuclear & Quantum Physics

5.1Discrete Energy & Radioactivity

5.1.1Atomic Spectra

5.1.2Atomic Structure

5.1.3Photons

5.1.4Discrete Energy Levels

5.1.5Alpha, Beta & Gamma Radiation

5.1.6Scientific Practices - Unstable Nuclei

5.1.7Radioactive Decay

5.1.8IB Multiple Choice - Atomic Physics

5.2Nuclear Reactions

5.2.1Mass & Energy

5.2.2Nuclear Fission

5.3The Interaction of Matter with Radiation

5.3.1Particles, Antiparticles & Photons

5.3.2Particle Interactions

5.3.3Classification of Particles

5.3.4Wave-Particle Duality

5.3.5Wave Functions & Probability

5.3.6IB Multiple Choice - Quantum Physics

5.4Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay

5.4.2Nuclear Radius

5.4.3IB Multiple Choice - Nuclear Physics

6Measurements

6.1Measurements & Errors

6.1.1Fundamental Units

6.1.2SI Prefixes, Standard Form & Converting Units

6.1.3End of Topic Test - Units & Prefixes

6.2Uncertainties & Errors

6.2.1Limitation of Physical Measurements

6.2.2Uncertainty

6.2.3Estimation

6.2.4End of Topic Test - Measurements & Errors

6.3Vectors & Scalars

6.3.1Scalars & Vectors

6.3.2Vector Problems

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