4.1.2

Centripetal Force

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Centripetal Acceleration

Acceleration is a change in the direction or magnitude of the velocity. In a circle, the velocity is always changing. This means that the object is always accelerating.

Change in velocity

Change in velocity

We can use vectors to find the change in velocity of an object between two points.
If we make a triangle of vectors with the initial and final velocity we see that the change in velocity is always pointing towards the centre.
In circular motion, the acceleration always points towards the centre of the circle.

Centripetal acceleration

Centripetal acceleration

The acceleration in circular motion is always directed towards the centre of the circle, this is because the change in velocity is directed towards the centre.
- Acceleration = change in velocity ÷ change in time
- $a{_c}={\Delta}v\;{\div}\;{\Delta}t$
This is called centripetal acceleration.

Calculating acceleration

Calculating acceleration

Centripetal acceleration can be found using linear or angular quantities:
- $a{_c}={\Delta}v\;{\div}\;{\Delta}t$
- $a{_c}=v^2 {\div} r$
- $a{_c}=r{\omega}^2$

Centripetal Force

Any force which causes circular motion is known as a centripetal force. The larger the centripetal force, the smaller the circle.

Forces towards the centre

Forces towards the centre

The direction of centripetal force is always towards the centre of the circle.
Any combination of forces can cause a centripetal force, for example, the earth's gravity on the moon.
Centripetal force is always perpendicular to the instantaneous velocity.

Calculating centripetal force

Calculating centripetal force

According to Newton's second law of motion, the net force is mass times acceleration.
- $F{_c}=ma{_c}$
By substituting in the equation $a{_c}=v^2/r$
- $F{_c}=mv^2/r$
  - Where m is the mass of the object.

1

Space, Time & Motion

1.1

Motion

1.1.1Motion Basics 1.1.2Graphs of Motion 1.1.3Uniform Acceleration Equations 1.1.4Projectile Motion 1.1.5Bouncing Ball Example

1.2

Forces

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

1.3

Momentum & Impulse

1.3.1Momentum 1.3.2Momentum 2 1.3.3End of Topic Test - Newton's Laws & Momentum

1.4

Work, Energy & Power

1.4.1Work & Energy 1.4.2Conservation of Energy 1.4.3Power & Efficiency 1.4.4IB Multiple Choice- Work, Energy & Power

2

The Particulate Nature of Matter

2.1

Thermal 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

2.2

Modelling 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

3

Wave Behaviour

3.1

Oscillations

3.1.1Progressive Waves 3.1.2Simple Harmonic Motion

3.2

Travelling 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

3.3

Wave Characteristics

3.3.1Polarisation

3.4

Wave Behaviour

3.4.1Reflection & Absorption 3.4.2Reflection of Light 3.4.3Refraction 3.4.4Refractive index

3.5

Standing Waves

3.5.1Standing Waves 3.5.2Standing Waves 2 3.5.3End of Topic Test - Standing Waves 3.5.4IB Multiple Choice - Waves

3.6

Simple 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

3.7

Single Slit Diffraction

3.7.1Diffraction

3.8

Interference

3.8.1Interference 3.8.2Interference 2 3.8.3Diffraction Gratings 3.8.4End of Topic Test - Diffraction

3.9

Doppler Effect

3.9.1Doppler Effect

4

Fields

4.1

Circular Motion

4.1.1Circular Motion 4.1.2Centripetal Force 4.1.3IB Multiple Choice - Circular Motion

4.2

Newton'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

4.3

Fields

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

4.4

Fields 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

4.5

Electric 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

4.6

Magnetic 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

4.7

Heating Effect of Currents

4.7.1Circuits 4.7.2Resistance 4.7.3Power and Conservation 4.7.4IB Multiple Choice - DC Circuits

4.8

Electromagnetic Induction

4.8.1Electromagnetic Induction 4.8.2Electromagnetic Induction 2 4.8.3Magnetic Flux & Flux Linkage 4.8.4End of Topic Test - Electromagnetic Induction

4.9

Power Generation & Transmission

4.9.1Alternating Currents 4.9.2Operation of a Transformer

4.10

Capacitance

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

5

Nuclear & Quantum Physics

5.1

Discrete 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

5.2

Nuclear Reactions

5.2.1Mass & Energy 5.2.2Nuclear Fission

5.3

The 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

5.4

Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay 5.4.2Nuclear Radius 5.4.3IB Multiple Choice - Nuclear Physics

6

Measurements

6.1

Measurements & Errors

6.1.1Fundamental Units 6.1.2SI Prefixes, Standard Form & Converting Units 6.1.3End of Topic Test - Units & Prefixes

6.2

Uncertainties & Errors

6.2.1Limitation of Physical Measurements 6.2.2Uncertainty 6.2.3Estimation 6.2.4End of Topic Test - Measurements & Errors

6.3

Vectors & Scalars

6.3.1Scalars & Vectors 6.3.2Vector Problems

Jump to other topics

1

Space, Time & Motion

1.1

Motion

1.1.1Motion Basics 1.1.2Graphs of Motion 1.1.3Uniform Acceleration Equations 1.1.4Projectile Motion 1.1.5Bouncing Ball Example

1.2

Forces

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

1.3

Momentum & Impulse

1.3.1Momentum 1.3.2Momentum 2 1.3.3End of Topic Test - Newton's Laws & Momentum

1.4

Work, Energy & Power

1.4.1Work & Energy 1.4.2Conservation of Energy 1.4.3Power & Efficiency 1.4.4IB Multiple Choice- Work, Energy & Power

2

The Particulate Nature of Matter

2.1

Thermal 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

2.2

Modelling 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

3

Wave Behaviour

3.1

Oscillations

3.1.1Progressive Waves 3.1.2Simple Harmonic Motion

3.2

Travelling 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

3.3

Wave Characteristics

3.3.1Polarisation

3.4

Wave Behaviour

3.4.1Reflection & Absorption 3.4.2Reflection of Light 3.4.3Refraction 3.4.4Refractive index

3.5

Standing Waves

3.5.1Standing Waves 3.5.2Standing Waves 2 3.5.3End of Topic Test - Standing Waves 3.5.4IB Multiple Choice - Waves

3.6

Simple 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

3.7

Single Slit Diffraction

3.7.1Diffraction

3.8

Interference

3.8.1Interference 3.8.2Interference 2 3.8.3Diffraction Gratings 3.8.4End of Topic Test - Diffraction

3.9

Doppler Effect

3.9.1Doppler Effect

4

Fields

4.1

Circular Motion

4.1.1Circular Motion 4.1.2Centripetal Force 4.1.3IB Multiple Choice - Circular Motion

4.2

Newton'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

4.3

Fields

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

4.4

Fields 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

4.5

Electric 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

4.6

Magnetic 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

4.7

Heating Effect of Currents

4.7.1Circuits 4.7.2Resistance 4.7.3Power and Conservation 4.7.4IB Multiple Choice - DC Circuits

4.8

Electromagnetic Induction

4.8.1Electromagnetic Induction 4.8.2Electromagnetic Induction 2 4.8.3Magnetic Flux & Flux Linkage 4.8.4End of Topic Test - Electromagnetic Induction

4.9

Power Generation & Transmission

4.9.1Alternating Currents 4.9.2Operation of a Transformer

4.10

Capacitance

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

5

Nuclear & Quantum Physics

5.1

Discrete 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

5.2

Nuclear Reactions

5.2.1Mass & Energy 5.2.2Nuclear Fission

5.3

The 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

5.4

Nuclear Physics

5.4.1Nuclear Instability & Radioactive Decay 5.4.2Nuclear Radius 5.4.3IB Multiple Choice - Nuclear Physics

6

Measurements

6.1

Measurements & Errors

6.1.1Fundamental Units 6.1.2SI Prefixes, Standard Form & Converting Units 6.1.3End of Topic Test - Units & Prefixes

6.2

Uncertainties & Errors

6.2.1Limitation of Physical Measurements 6.2.2Uncertainty 6.2.3Estimation 6.2.4End of Topic Test - Measurements & Errors

6.3

Vectors & Scalars

6.3.1Scalars & Vectors 6.3.2Vector Problems

Practice questions on Centripetal Force

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1
What direction is the centripetal acceleration of circular motion in?Multiple choice
2
What is the equation for centripetal acceleration?Multiple choice
3
In what direction does centripetal force act?Multiple choice
4
What is the correct form of the equation for centripetal force?Multiple choice

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Circular Motion

IB Multiple Choice - Circular Motion