Conservation Laws in Physics

Overview

Conservation Laws in Physics explains the fundamental quantities that remain constant during physical processes in isolated systems.

Conservation laws are powerful because they allow prediction of outcomes even when the detailed mechanism is complicated.

They are especially important in:

• mechanics
• collisions
• electric circuits
• waves
• nuclear reactions
• particle interactions

In H2 Physics, conservation laws are widely used to solve problems efficiently.

Core Ideas

• conservation laws place strong restrictions on what can happen in a physical process
• energy can be transferred or transformed but total energy remains constant in an isolated system
• momentum is conserved in an isolated system with no external resultant force
• charge is conserved in electric and nuclear processes
• nucleon number and proton number must balance in H2 nuclear equations
• mass is not separately conserved in modern physics; the deeper law is mass-energy conservation

Why Conservation Laws Matter

A physical process may involve:

• forces changing motion
• energy transfer
• particle transformation
• collisions
• decay

Even when details are complex, certain total quantities remain constant.

This provides strong constraints on what can and cannot happen.

Main Conservation Laws in H2 Physics

1. Conservation of Energy

Energy cannot be created or destroyed.

It can only be transferred or transformed.

Examples:

• gravitational potential energy to kinetic energy
• chemical energy to thermal energy
• electrical energy to light
• mass defect to nuclear energy

General idea:

$$\text{Total energy before}=\text{Total energy after}$$

For the broader treatment of energy forms and transfers, see Energy Forms and Conservation and Work, Energy and Power.

2. Conservation of Linear Momentum

In an isolated system with no external resultant force:

$$\text{Total momentum before}=\text{Total momentum after}$$

Where momentum is:

$$\vec{p}=m\vec{v}$$

Momentum is a vector, so direction matters.

It is used in:

• collisions
• explosions
• recoil
• nuclear decay

For more on system-level collision reasoning, see Momentum Conservation and Collisions.

3. Conservation of Charge

Total electric charge remains constant.

Example:

Before:

• neutral atom = 0

After ionisation:

• positive ion + electron

Total charge remains unchanged.

It is used heavily in:

• electric circuits
• electrostatics
• particle decay
• nuclear equations

4. Conservation of Nucleon Number

In nuclear reactions, the total nucleon number $A$ is conserved at H2 level.

Where:

• proton = 1 nucleon
• neutron = 1 nucleon

Example:

$${}_6^{14}\text{C}\to {}_7^{14}\text{N}+{}_{-1}^{0}e$$

Top numbers:

$$14=14+0$$

5. Conservation of Proton Number

Total proton number $Z$, equivalently total charge, is conserved.

Example:

$${}_6^{14}\text{C}\to {}_7^{14}\text{N}+{}_{-1}^{0}e$$

Bottom numbers:

$$6=7+(-1)$$

Conservation of Mass

In classical physics, mass is often treated as conserved.

However, in modern physics:

• mass may convert to energy
• energy contributes to the total mass-energy accounting

So the deeper law is mass-energy conservation:

$$E=m{c}^2$$

This matters especially in nuclear physics.

Applications in Mechanics

Collisions

For isolated systems:

$$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$$

Types of Collision

Elastic Collision

• momentum conserved
• kinetic energy conserved

Inelastic Collision

• momentum conserved
• kinetic energy not conserved

Explosions and Recoil

Initial momentum may be zero.

After separation:

• total momentum is still zero

Example:

Gun recoil:

• bullet forward momentum
• gun backward momentum

Figure: Recoil after an explosion.

Applications in Nuclear Physics

Conservation laws determine valid nuclear equations.

Example: Alpha Decay

$${}_{92}^{238}\text{U}\to {}_{90}^{234}\text{Th}+{}_2^4\text{He}$$

Check:

• nucleon number conserved
• proton number conserved
• energy conserved
• momentum conserved

Example: Beta Decay

$${}_6^{14}\text{C}\to {}_7^{14}\text{N}+{}_{-1}^{0}e+\bar{\nu }$$

The antineutrino helps conserve:

• energy
• momentum

A full lepton-number treatment is beyond the H2 scope of this wiki.

Applications in Circuits

Charge Conservation at a Junction

Current entering a junction equals current leaving it.

Kirchhoff’s first law:

$$\sum I_{\text{in}}=\sum I_{\text{out}}$$

Figure: Current conservation at a junction.

This is used heavily in DC Circuits.

Applications in Waves

Energy Conservation

Wave energy is transferred from a source to a medium or field.

Examples:

• electrical energy to sound
• electrical energy to electromagnetic radiation

How to Use Conservation Laws in Questions

Step 1: Identify the System

Choose the object, collection of objects, or particles involved.

Step 2: Identify Whether It Is Isolated

Ask whether significant external forces or external energy transfers are present.

Step 3: Choose the Relevant Law

Ask which of these is useful:

• momentum
• energy
• charge
• nucleon number
• proton number

Step 4: Write Before = After

Set up equations carefully.

Common Exam Examples

Example 1: Collision

Two carts stick together.

Use:

• momentum conserved

Do not assume kinetic energy is conserved.

Example 2: Nuclear Equation

$${}_{88}^{226}\text{Ra}\to ?+{}_2^4\text{He}$$

Use:

• $A$: $226-4=222$
• $Z$: $88-2=86$

Answer:

$${}_{86}^{222}\text{Rn}$$

Example 3: Junction Current

3 A enters a node. One branch carries 1 A.

Remaining branch:

$$2\text{ A}$$

Exam Relevance

This topic is especially useful for:

• nuclear equations
• radioactive decay processes
• fission and fusion reactions
• collisions and recoil
• current-junction reasoning
• energy-transfer problems

Common mistakes include:

• applying momentum conservation to one object instead of a system
• assuming kinetic energy is always conserved
• forgetting direction in momentum
• forgetting charge balance in beta decay
• treating mass as separately conserved in nuclear reactions

Quick Comparison Table

Quantity	Conserved When
Energy	Isolated system when all forms are counted
Momentum	No external resultant force on the system
Charge	Always observed
Nucleon number	Nuclear reactions at H2 level
Proton number	Nuclear reactions

Quick Revision Summary

• conservation laws strongly restrict physical outcomes
• energy can transform but total remains constant
• momentum is conserved in isolated systems
• charge is conserved
• nuclear equations must conserve $A$ and $Z$
• conservation laws help solve unseen problems efficiently

Links

• Prerequisite: energy forms and conservation
• Prerequisite: dynamics
• Related: work energy and power
• Related: dc circuits
• Related: momentum conservation and collisions
• Related: nuclear physics
• Related: radioactive decay
• Related: particle physics
• Related: nuclear fission
• Related: nuclear fusion