Newton's Laws of Motion - Understanding How Forces Affect The Movement of Objects in Our Everyday Lives
Newton's Laws of Motion form the foundation of classical mechanics, describing how objects move and interact under the influence of forces. These laws explain the behaviour of stationary and moving bodies, making them essential for understanding everything from everyday motions to complex mechanical systems. Sir Isaac Newton formulated the laws of motion in the year 1686 in his book ‘Principia Mathematica Philosophiae Naturalis. In this guide, we’ll explore the three laws, their applications, and how they help us analyse motion in various scenarios for JEE Main 2025.
What are Newton's Laws of Motion?
The Three Newtons Laws of Motion are:
Newton’s first law (Law of Inertia) - Newton's first law of motion states that, if a body is in the state of rest or is moving with a constant speed in a straight line, then the body will remain in the state of rest or keep moving in the straight line, unless and until it is acted upon by an external force.
Newton’s second law (Force and Acceleration) - Newton's 2nd law of motion states that the rate of change of momentum of a body is directly proportional to the force applied on it, and the momentum occurs in the direction of the net applied force.
Newton’s third law (Action-Reaction) - According to Newton's third law of motion, to every action, there is always an equal and opposite reaction.
First Law of Motion (Law of Inertia)
This property of a body unable to change its state is called Inertia. Galileo Galilei first formulated the law of inertia for the horizontal motion of planet Earth. Later on, it was generalised to René Descartes. Before Galileo, it was believed that a force is required to keep a body moving. Galileo deduced that a body can't change its state unless acted by force (like friction).
The state of motion or rest cannot be changed without applying force. If a body is moving in a particular direction, it will keep moving in that direction, until an external force is applied to stop it.
Second Law of Motion (F=MA)
Newton's second law gives a quantitative description of force. The momentum of a body is equivalent to the product of its mass and velocity. To speak, momentum is a vector quantity having both velocity and magnitude. When force is applied to a body, it can either change its momentum, its velocity or both. Newton's second law of motion is one of the most important laws of classical physics.
For a body of constant mass m, Newton's law formula is given as,
F = ma,
Where ‘F’ is the applied force, and ‘a’ is the acceleration produced, and m is the mass of the object
If the net force acting on a body is positive, the body gets accelerated. Conversely, if the net force is 0, the body doesn't accelerate.
According to the second law of motion, if force is applied to two different objects of different masses, different accelerations (change in motion) are produced. The body with less mass accelerates more.
The effect of a force of around 15 Newton on football will be much more significant as compared to the impact of the same force applied to move a car. This difference is due to the difference in the masses of the two objects.
Third Law of Motion (Action-Reaction)
According to Newton's third law of motion, to every action, there is always an equal and opposite reaction. Also, the action and reaction occur in two different bodies. When two bodies interact with each other, they exchange force, which is equal in magnitude but act in opposite directions. This law has a huge application in static equilibrium where the forces are balanced, and also for objects which undergo uniform accelerated motion.
For example, a laptop kept on a table exerts a downward force, which is equal to its weight on the table, and consequently, the table exerts an equal and opposite force on the laptop. This force comes into play because the weight of the laptop slightly deforms the table, and in return, the table pushes back the laptop.
Newtons Laws of Motion Examples
Here are simple examples to help understand Newton's three laws of motion:
1. Newton's First Law (Law of Inertia):
Example: A stationary ball on a flat surface will stay at rest until someone kicks it. Similarly, a moving car will keep moving unless brakes are applied or another force stops it.
Real Life: Wearing seat belts in a car prevents passengers from moving forward during a sudden stop.
2. Newton's Second Law (Force and Acceleration):
Example: A shopping trolley accelerates faster when pushed with more force. A heavier trolley needs more force to move it at the same speed.
Real Life: A cricketer applies less force to throw a tennis ball than a cricket ball because the cricket ball is heavier.
3. Newton's Third Law (Action and Reaction):
Example: When you jump off a small boat, the boat moves backwards as you push it. Your push (action) causes the boat to move in the opposite direction (reaction).
Real Life: Rockets launch into space by pushing exhaust gases downward, which causes the rocket to move upward.
Newtons Laws of Motion Equations
1. Newton's First Law (Law of Inertia):
$\text{If } \mathbf{F_{net}} = 0, \text{ then } \mathbf{v = constant}$
$\mathbf{F_{net}}$: Net external force acting on the object
$\mathbf{v}$: Velocity of the object
2. Newton's Second Law (F = ma):
$\mathbf{F = ma}$
$\mathbf{F}$: Net force acting on the object (in Newtons, N)
$\mathbf{m}$: Mass of the object (in kilograms, kg)
$\mathbf{a}$: Acceleration of the object (in meters per second squared, m/s²)
3. Newton's Third Law (Action and Reaction):
$\mathbf{F_{12} = -F_{21}}$
$\mathbf{F_{12}}$: Force exerted by object 1 on object 2
$\mathbf{F_{21}}$: Force exerted by object 2 on object 1
Additional Equations:
Equations of Motion (from Second Law):
v=u+at
v: Final velocity of the object
u: Initial velocity of the object
a: Acceleration of the object
t: Time taken
$s = ut + \frac{1}{2}at^2$
s: Displacement of the object
u: Initial velocity
a: Acceleration
t: Time taken
$v^2 = u^2 + 2as$
v: Final velocity
u: Initial velocity
a: Acceleration
s: Displacement
Newton Laws of Motions Numericals
Numerical 1: Newton’s First Law (Law of Inertia)
Question: A car is moving at a constant speed of 20 m/s. If the brakes are applied, causing the car to stop in 5 seconds, calculate the acceleration of the car.
Solution:
Initial speed, $u = 20 \, \text{m/s}$
Final speed, $v = 0 \, \text{m/s}$
Time, t=5 seconds
Using the equation of motion:
v=u+at
$0 = 20 + a \times 5$
$a = \dfrac{-20}{5} = -4 \, \text{m/s}^2$
The car’s acceleration is $-4 \, \text{m/s}^2$, where the negative sign indicates deceleration.
Numerical 2: Newton’s Second Law (F = ma)
Question: A 10 kg object is acted upon by a force of 50 N. Find the acceleration of the object.
Solution:
Mass, $m = 10 \, \text{kg}$
Force, $F = 50 \, \text{N}$
Using Newton’s Second Law:
F=ma
$50 = 10 \times a$
$a = \dfrac{50}{10} = 5 \, \text{m/s}^2$
The acceleration of the object is $5 \, \text{m/s}^2$.
Numerical 3: Newton’s Third Law (Action-Reaction)
Question: A person is standing on a boat. If the person jumps off the boat with a force of 30 N, what is the reaction force exerted on the boat?
Solution: According to Newton’s Third Law, for every action, there is an equal and opposite reaction.
Action force (person jumping) =$30 \, \text{N}$
Reaction force (boat's movement) = $30 \, \text{N}$ in the opposite direction.
Thus, the boat will move backwards with a force of $30 \, \text{N}$.
Applications of Newton's Laws
Seat belts stop passengers from continuing to move forward when the car suddenly stops.
The force used in sports (like kicking a ball or throwing a shot put) depends on the mass of the object and how fast it needs to accelerate.
Rockets move upwards by pushing gases downwards with an equal and opposite force.
When you push your foot back on the ground, the ground pushes you forward.
When you push down on the ground to jump, the ground pushes you upwards with the same force.
Conclusion
Newton's Laws of Motion are fundamental principles that explain how objects move and interact with forces. The First Law shows that objects resist changes in motion, the Second Law connects force, mass, and acceleration, and the Third Law highlights the action-reaction pairs in every force interaction. These laws not only help us understand everyday movements but also form the basis for engineering, technology, and space exploration. By mastering these laws, we can better understand the physical world and the forces that drive it.
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FAQs on Newton’s Laws of Motion: Three Laws of Motion Explanation with Examples
1. What are Newton's three laws of motion and their standard mathematical forms relevant for JEE Main 2026?
Newton's three laws of motion are fundamental principles of classical mechanics. For JEE Main preparation, it's crucial to understand them both conceptually and mathematically:
- Newton's First Law (Law of Inertia): An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied external force. Mathematically, if the net external force F_net is zero, then the velocity v is constant (F_net = 0 ⇒ v = constant).
- Newton's Second Law (Law of Acceleration): The rate of change of linear momentum of a body is directly proportional to the applied external force, and this change takes place in the direction of the force. The most common form is F = ma, where F is the net force, m is mass, and a is acceleration. The more fundamental form is F = dp/dt.
- Newton's Third Law (Action-Reaction): For every action, there is always an equal and opposite reaction. If object 1 exerts a force F_12 on object 2, then object 2 exerts an equal and opposite force F_21 on object 1, such that F_12 = -F_21.
2. In Newton's Third Law, if action and reaction forces are equal and opposite, why don't they cancel each other out?
This is a common misconception. The action and reaction forces never cancel each other out because they act on two different objects. For forces to cancel, they must act on the same object. For example, when a book rests on a table, the book exerts a downward force (action) on the table. The table exerts an upward force (reaction) on the book. Since one force acts on the table and the other on the book, they cannot be added together to get a net force of zero on a single body.
3. What is the difference between an inertial and a non-inertial frame of reference?
The distinction between inertial and non-inertial frames is a critical concept for solving JEE problems:
- An inertial frame of reference is one that is either at rest or moving with a constant velocity. In these frames, Newton's first law holds true, and no fictitious forces are needed to explain motion. The laws of physics are in their simplest form here.
- A non-inertial frame of reference is one that is accelerating. In these frames, Newton's first law does not hold. To apply Newton's laws, we must introduce the concept of pseudo forces (or fictitious forces) that act in the direction opposite to the frame's acceleration. For example, the feeling of being pushed back in an accelerating car is due to a pseudo force.
4. How is Newton's Second Law applied to systems with variable mass, like a rocket?
For systems where the mass changes with time, such as a rocket ejecting fuel, the standard form F = ma is insufficient. The more fundamental version of Newton's second law, F_net = dp/dt = d(mv)/dt, must be used. Applying the product rule gives F_net = m(dv/dt) + v(dm/dt). For a rocket, this equation helps calculate the thrust, which is the force generated by expelling mass. The term v(dm/dt) represents the thrust force due to the ejection of fuel, which is crucial for determining the rocket's acceleration.
5. How do you apply Newton's laws to solve problems involving connected bodies, like blocks on a table or in an Atwood machine?
To solve problems with connected bodies, a systematic approach is used:
- Isolate each body: Treat each mass in the system as a separate object.
- Draw Free-Body Diagrams (FBDs): For each isolated mass, draw all the external forces acting on it, such as gravity (mg), tension (T), normal force (N), and friction (f).
- Apply Newton's Second Law: Write the F = ma equation for each body along the relevant axes of motion. Remember that for connected bodies, the magnitude of acceleration is typically the same for all parts of the system.
- Solve the system of equations: You will get a set of simultaneous linear equations which can be solved to find unknown quantities like acceleration and tension.
6. Why is Newton's Second Law more accurately expressed as F = dp/dt instead of F = ma?
While F = ma is widely used and correct for systems with constant mass, F = dp/dt (where p is momentum, p=mv) is the more universal and fundamental statement of the law. This is because it correctly describes motion even when the mass of the system is changing, such as in rocket propulsion or a conveyor belt being loaded with sand. F = ma is a special case of F = dp/dt that applies only when mass (m) is constant, allowing it to be taken out of the derivative.
7. How is the principle of conservation of linear momentum derived from Newton's Laws?
The principle of conservation of linear momentum is a direct consequence of Newton's second and third laws. According to Newton's second law, the net external force on a system is equal to the rate of change of its linear momentum (F_ext = dp/dt). If the net external force on a system is zero (F_ext = 0), then dp/dt = 0. This implies that the momentum (p) of the system does not change with time; it remains constant. Therefore, in an isolated system where no external forces are acting, the total linear momentum is conserved.
8. What are the key limitations of Newton's Laws of Motion?
While foundational to classical mechanics, Newton's laws have limitations and are not universally applicable. They fail under two main conditions:
- Objects at very high speeds: When an object's speed approaches the speed of light (c), its behaviour is described by Einstein's Theory of Special Relativity, not Newtonian mechanics. Mass, time, and length are no longer absolute at these speeds.
- Objects at the atomic or subatomic scale: The motion and behaviour of particles like electrons and photons are governed by the principles of Quantum Mechanics. Newtonian physics cannot explain phenomena like wave-particle duality or quantum tunnelling.
