Newton’s Laws of Motion

1. Introduction

Newton’s laws of motion are three fundamental principles of classical mechanics that explain the relationship between the motion of an object and the forces acting upon it.

They were formulated by the English physicist Sir Isaac Newton and published in his work Philosophiæ Naturalis Principia Mathematica in 1687.

These laws form the foundation of classical mechanics and explain many everyday phenomena, including walking, driving, falling objects, collisions and the movement of vehicles.

The three laws are:

1. Law of inertia.
2. Law of acceleration.
3. Law of action and reaction.

2. Force

Force is an interaction that can change or tend to change the state of motion, direction or shape of an object.

Force is a vector quantity.

The SI unit of force is the newton (N).

One newton is the force required to accelerate a mass of one kilogram at one metre per second squared.

[
1\ N=1\ kg\cdot m/s^2
]

2.1 Types of force

Forces may be classified as contact or non-contact forces.

Contact forces require physical contact between interacting objects.

Examples:

• Frictional force.
• Normal reaction.
• Tension.
• Applied force.
• Air resistance.
• Spring force.

Non-contact forces act without direct physical contact.

Examples:

• Gravitational force.
• Magnetic force.
• Electrostatic force.

3. Newton’s First Law of Motion: Law of Inertia

Newton’s first law states:

An object remains at rest or continues moving with constant velocity in a straight line unless acted upon by a net external force.

This law explains the concept of inertia.

3.1 Inertia

Inertia is the tendency of an object to resist any change in its state of rest or uniform motion in a straight line.

Mass is a measure of an object’s inertia.

A heavier object generally has greater inertia than a lighter object.

3.2 Types of inertia

Inertia of rest: The tendency of an object at rest to remain at rest.

Example: When a stationary bus suddenly starts moving, passengers tend to fall backwards because their bodies initially resist the change in motion.

Inertia of motion: The tendency of a moving object to continue moving with constant velocity.

Example: When a moving bus suddenly stops, passengers tend to move forward.

Inertia of direction: The tendency of an object to resist a change in its direction of motion.

Example: Passengers in a moving car tend to lean sideways when the car takes a sharp turn.

3.3 Everyday applications of the first law

1. Seat belts protect passengers when a vehicle suddenly stops.
2. Dust is removed from carpets by beating or shaking them.
3. Passengers move forward when a moving bus stops suddenly.
4. A coin placed on a card falls into a glass when the card is quickly pulled away.
5. A rolling ball continues moving until friction and other forces slow it down.

3.4 Inertia and mass

Greater mass means greater resistance to changes in motion.

For example, pushing a stationary truck requires more force to produce the same acceleration as pushing a small trolley, assuming other conditions are comparable.

4. Newton’s Second Law of Motion: Law of Acceleration

Newton’s second law states that the net external force acting on an object is equal to the rate of change of its momentum.

For constant mass, this becomes the familiar relationship between net force, mass and acceleration.

[
F_{\text{net}}=ma
]

Where:

• (F_{\text{net}}) = net external force in newtons
• (m) = mass in kilograms
• (a) = acceleration in m/s²

4.1 Explanation

The acceleration of an object:

1. Is directly proportional to the net force acting upon it, when mass is constant.
2. Is inversely proportional to its mass, when net force is constant.
3. Occurs in the direction of the net force.

4.2 Example: Calculating force

A body of mass 5 kg accelerates at 3 m/s².

[
F=ma
]

[
F=5\times3=15\ N
]

The net force is 15 newtons.

4.3 Example: Calculating acceleration

A force of 40 N acts on an object of mass 8 kg.

[
a=\frac{F}{m}
]

[
a=\frac{40}{8}=5\ m/s^2
]

The acceleration is 5 m/s².

4.4 Net force and balanced forces

The net force is the vector sum of all forces acting on an object.

If two equal and opposite forces act on an object, their resultant is zero.

For example, if a box is pushed to the right with 20 N while friction acts to the left with 20 N, the net horizontal force is zero.

The object therefore has no horizontal acceleration. It may remain at rest or continue moving at constant velocity.

Important: Zero net force does not necessarily mean zero velocity.

5. Newton’s Third Law of Motion: Law of Action and Reaction

Newton’s third law states:

For every action, there is an equal and opposite reaction.

When two bodies interact, each exerts a force on the other. These forces are equal in magnitude and opposite in direction.

5.1 Characteristics of action and reaction forces

1. They are equal in magnitude.
2. They act in opposite directions.
3. They occur simultaneously.
4. They act on different bodies.
5. They are of the same type of interaction.

Because they act on different bodies, action and reaction forces do not cancel each other when considering the motion of a single body.

5.2 Everyday examples

Walking: A person pushes the ground backwards, and the ground exerts a forward frictional force on the person.

Swimming: A swimmer pushes water backwards, and the water exerts a forward force on the swimmer.

Rocket propulsion: A rocket expels exhaust gases backwards, and the gases exert a forward force on the rocket.

Gun recoil: A bullet moves forward while the gun experiences backward recoil.

Jumping: A person pushes the ground downward, and the ground exerts an upward force.

6. Comparison of Newton’s Three Laws

7. Applications of Newton’s Laws

7.1 Seat belts and vehicle safety

When a vehicle suddenly stops, passengers tend to continue moving forward because of inertia.

Seat belts provide the force needed to change the passengers’ motion and reduce the risk of injury.

Airbags increase the time over which a passenger’s momentum is reduced, helping lower the average force experienced during a collision.

7.2 Rocket propulsion

A rocket moves forward by expelling gases at high speed in the opposite direction.

This illustrates Newton’s third law and the conservation of momentum.

Rockets can operate in the vacuum of space because they do not need to push against air. They expel their own propellant mass.

7.3 Recoil of firearms

When a projectile is accelerated forward, the firearm experiences a backward reaction.

The recoil velocity depends on the masses and velocities involved.

7.4 Walking and running

A person applies a backward force to the ground through friction. The ground applies a forward force on the person.

Without sufficient friction, walking becomes difficult, as demonstrated by slipping on an icy surface.

7.5 Vehicle acceleration

A vehicle accelerates when the net forward force is greater than the opposing forces, such as rolling resistance and air resistance.

If the driving force and resistive forces balance, the vehicle can move at constant velocity.

8. Newton’s Second Law and Momentum

Momentum is the product of mass and velocity.

[
p=mv
]

Newton’s second law can be expressed in its general form:

[
F_{\text{net}}=\frac{\Delta p}{\Delta t}
]

For an instantaneous rate of change:

[
F_{\text{net}}=\frac{dp}{dt}
]

For constant mass:

[
F_{\text{net}}=ma
]

This shows that the familiar force-acceleration equation is a special case of the more general momentum form of Newton’s second law.

9. Newton’s Laws and Gravitation

Newton’s law of universal gravitation states that every two objects with mass attract each other through a gravitational force.

The magnitude of this force is:

[
F=G\frac{m_1m_2}{r^2}
]

Where:

• (F) = gravitational force
• (G) = universal gravitational constant
• (m_1) and (m_2) = masses of the two objects
• (r) = distance between their centres

The gravitational force increases with the product of the masses and decreases with the square of the distance between their centres.

Newtonian gravitation explains many phenomena, including falling objects, planetary orbits and satellite motion, within its range of validity.

10. Limitations of Newtonian Mechanics

Newton’s laws are highly accurate for everyday objects and ordinary speeds, but they are not universally sufficient.

10.1 Very high speeds

At speeds approaching the speed of light, classical Newtonian mechanics must be replaced by relativistic mechanics for accurate results.

10.2 Atomic and subatomic scales

At atomic and subatomic scales, quantum mechanics is required.

10.3 Strong gravitational fields

In situations involving very strong gravitational fields or high precision, general relativity provides a more accurate description than Newtonian gravity.

11. Important Examination Concepts

Inertia versus momentum: Inertia is resistance to changes in motion and is associated with mass. Momentum depends on both mass and velocity.

Balanced versus unbalanced forces: Balanced forces produce zero resultant force. Unbalanced forces produce acceleration.

Action and reaction: They act on different bodies, not on the same body.

Constant velocity: An object moving at constant velocity has zero acceleration and zero net external force in an inertial frame.

36 Key Takeaways for Exams

1. Sir Isaac Newton formulated the three laws of motion.
2. Newton published his laws in Principia Mathematica in 1687.
3. Force is an interaction that can change an object’s motion or shape.
4. The SI unit of force is the newton.
5. One newton equals one kilogram metre per second squared.
6. Newton’s first law is also known as the law of inertia.
7. Inertia is resistance to a change in the state of motion.
8. Mass is a measure of inertia.
9. Greater mass generally means greater inertia.
10. Inertia of rest is the tendency to remain at rest.
11. Inertia of motion is the tendency to continue moving.
12. Inertia of direction is resistance to a change in direction.
13. Seat belts help protect passengers because of inertia.
14. Newton’s second law relates net force to the rate of change of momentum.
15. For constant mass, the second law is expressed as net force equals mass multiplied by acceleration.
16. Acceleration is directly proportional to net force for constant mass.
17. Acceleration is inversely proportional to mass for constant net force.
18. The direction of acceleration is the direction of the net force.
19. Net force is the vector sum of all forces acting on a body.
20. Zero net force means zero acceleration, not necessarily zero velocity.
21. Newton’s third law is known as the law of action and reaction.
22. Action and reaction forces are equal in magnitude.
23. Action and reaction forces act in opposite directions.
24. Action and reaction forces act on different bodies.
25. Walking illustrates Newton’s third law.
26. Rocket propulsion illustrates Newton’s third law and momentum conservation.
27. Gun recoil is an example of action and reaction.
28. Airbags increase the time over which momentum is reduced during a collision.
29. Momentum is the product of mass and velocity.
30. Newton’s second law in general form relates net force to the rate of change of momentum.
31. Newton’s law of universal gravitation describes attraction between masses.
32. Gravitational force is inversely proportional to the square of the distance between two centres.
33. Newtonian mechanics is highly effective for ordinary objects at everyday speeds.
34. Relativity is required for accurate descriptions at speeds approaching the speed of light.
35. Quantum mechanics is necessary for describing atomic and subatomic phenomena.
36. General relativity provides a more complete description of gravity in strong gravitational fields.