Conservation Laws in Physics: Definition, Derivations, Applications, Examples

Conservation laws in Physics are a principle based on experiments and observation, which cannot be proved. Some of the conserved quantities other than the main four (energy, mass, linear and angular momentum) are called spin, strangeness, baryon number, and so on.

The initial law of conservation of energy states that energy can neither be created nor be destroyed but only change from one form to another over time and remains constant. Similarly, many other laws are considered.

Keyterms: Energy, Mass, Linear and angular momentum, Initial law, Conservation, Spin, Strangeness, Baryon number

Read Also: Faraday’s Law of Electromagnetic Induction

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What are Conservation Laws in Physics?

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Conservation laws are explained below for your understanding:

Law Of Conservation Of Energy

This law states that, when a system is isolated from its surroundings, the energy of the system is always conserved.

• Energy is always constant with respect to time. 
• Energy can only transform from one form to another.
• The overall energy of the universe is never unchanged.

Examples: Kinetic energy, potential energy, chemical energy, and mechanical energy.

Examples of Kinetic and Potential Energy

Law of Conservation of Mass 

This law states that mass can neither be destroyed nor be created in a chemical reaction.

• Atoms rearrange themselves in different fashions among different molecules, in a chemical reaction, hence the mass remains constant.
• Since the mass remains constant, the total reactant mass and the total product mass remain the same.
• Chemical reactions can be both exothermic and endothermic.

Example: Carbon, being both solid and gas, holds the same mass and doesn’t change with the matter.

Example of Law of Conservation of Mass

Law of Conservation of Linear Momentum

This law states that in an isolated system when two objects collide the momentum of the system remains constant. The total linear momentum before and after the interaction remains the same.

Example: The gravitational force on the moon and the earth remains the same.

Law of Conservation of Angular Momentum

This law states that the total angular momentum of a system does not change and is conserved when the net external torque acting upon the system is null.

Example: A spin achieved by a skater on ice, Isotropy of space explains this law.

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Derivations of Conservation Laws:

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Here are some Derivations of Conservation Laws:

Mechanical Energy = Potential energy + kinetic energy 

E = U+K

• Potential energy is given by U = mgh, where m is mass, h is height and g is the gravity of earth.
• Kinetic energy is given by K =1/2 mv², it is the energy of the body in motion.

Consider a freely falling body,

The force exerted on the body is F= mg 

Now, if the body falling is from height H, the potential energy is U₁= mgH…(1)

The kinetic energy here is 0 as its speed is 0 and due to height.

Now, potential energy at time t and height h is, U₂ = mgh …(2)

Comparing (1) and (2)… change in potential energy (\(\bigtriangleup\)U)= U₁-U₂.

Considering the same body falling with speed v₁

F= ma and a (acceleration due to gravity) = v *dv/dx

F = m.v dv/dx

Now on integration on both sides,

\(\int F.dx=\int_{v1}^{v2}m.vdv\)

Here, F= mg and v1 and v2 is 0 and v respectively,

\(\int mg.dx=\int_{0}^{v}m.vdv\)

mgx = 1/2mv2

Let x be the displacement of the body, x = H-h

mg(H-h) = ½ mv2 = \(\bigtriangleup\)K

On comparing \(\bigtriangleup\)K and \(\bigtriangleup\)U, we infer that

\(\bigtriangleup\)K = -\(\bigtriangleup\)U…(3)

\(\bigtriangleup\)E = \(\bigtriangleup\)U+\(\bigtriangleup\)K

On substituting (3)

\(\bigtriangleup\)E = 0, states that energy is conserved.

Equation for Law of conservation of mass

E= mc², c is the speed of light.

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Things to Remember

• The general laws of conservation include, energy, mass, linear momentum and angular momentum.
• Conservation laws basically deal with the fundamental forces of nature. 
• The energy produced in conservation of mass is similar to Einstein’s theory, E= mc²
• Acceleration due to gravity on the moon is 1/6^th than that of the earth.
• The chemical reaction typically means atoms rearranging themselves among different molecules.
• The law of conservation of angular momentum explains the isotropy of space.

Read More: Energy Consideration Important Notes

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Previous Year Questions

1. A planet in a distant solar system is 10 times more massive … 
2. The speed of earth’s rotation about its axis is …
3. At what height above the …
4. Which of the following is true for rays coming from infinity? [DUET 2006]
5. A point source of light S, placed at a distance L in front of the centre of a plane mirror … [DUET 2000]
6. A girl of height 150 cm with her eye level at 140cm  … [KCET 2019]
7. A given ray of light suffers minimum deviation in an equilateral prism … [NEET 2001]
8. A biconvex lens has a radius of curvature of magnitude 20 cm. Which one of the …  [NEET 2011]
9.  Read the following statements … [AMUEEE 2009]
10. The nearest star to our solar system … [AMUEEE 2009]
11. The volume of a cube in … [DUET 2006]
12. What is dimensional formula of thermal conductivity … [DUET 2006]
13. In the formula … 
14. Two planets are revolving around the earth with velocities … 
15. Earth is revolving around the sun … ​
16. Imagine a new planet having the same density …