Laws of Motion for NEET and Class 11: Complete Guide with Examples

Laws of Motion is one of the most important chapters in NEET Physics and Class 11 Physics. It connects basic concepts like force and inertia to real‑life applications such as friction, collisions, and vehicles on curved and banked roads.

In this complete guide, you’ll learn:

• The three laws of motion (with NCERT‑style statements)

• Free‑body diagrams (FBDs) and how to draw them correctly

• Impulse and momentum, and when to use conservation of momentum

• Friction (static, kinetic, rolling) and common exam traps

• Uniform circular motion and banked road concepts are used in NEET questions

This article also includes representative NEET‑level examples so you can see how each idea is tested.

Force and Inertia: Historical Background: Aristotle vs Galileo

• Aristotle believed that a continuous force is required to keep an object in motion.

• Galileo used thought experiments to show that, in an ideal frictionless world, an object in motion would continue to move indefinitely even without a force.

This idea led to the law of inertia and laid the foundation for Newton’s First Law.

Definition of Inertia

Inertia is the property of a body to resist any change in its state of rest or of uniform motion in a straight line.

In NCERT language:`

• If the net external force on a body is zero, then:

• A body at rest remains at rest.

• A body in uniform motion continues with the same velocity.

NEET Shortcut: Zero Net Force Condition

Whenever a question mentions:

• “at rest”, or

• “moving with constant velocity”,

You can immediately write:

$\sum \vec F_{\text{ext}} = \vec 0 \Rightarrow \vec a = \vec 0$

This is one of the fastest ways to convert word problems into equations in NEET.

Newton’s Laws of Motion: Newton’s First Law of Motion (Law of Inertia)

Everybody continues in its state of rest or of uniform motion in a straight line unless it is compelled by an external force to act otherwise.

Equivalently:

• If the net external force = 0, then acceleration = 0.

Newton’s Second Law of Motion: Momentum Form of the Second Law

The most general form is:

$\vec F = \dfrac{d\vec p}{dt}$

where $\vec p = m\vec v$is momentum.

For constant mass m:

$\vec F = m\vec a$

This is the familiar F = ma form you use in most NEET problems.

SI Unit of Force

From $\vec F = m\vec a$:

• Mass unit: kg

• Acceleration unit: m s⁻²

So the SI unit of force is:

1 newton (1 N) = 1 kg·m·s⁻²

Newton’s Laws of Motion: Newton’s Third Law of Motion

Newton’s Third Law states that for every action, there is an equal and opposite reaction.

In simple words, whenever one body exerts a force on another body, the second body also exerts a force of the same magnitude and in the opposite direction on the first body.

Mathematically, $\vec F_{AB} = - \vec F_{BA} $.

Here:

• $\vec F_{AB} $is the force exerted by body A on body B

• $\vec F_{BA} $is the force exerted by body B on body A

Examples of Newton’s Third Law

• While walking, your foot pushes the ground backward, and the ground pushes you forward.

• A gun recoils backward when a bullet is fired forward.

• A swimmer pushes water backward, and water pushes the swimmer forward.

• A rocket moves upward because gases are expelled downward.

Free Body Diagram

A Free Body Diagram, or F.B.D., is a simplified diagram that shows all the external forces acting on a single object. It helps in identifying the forces clearly before applying Newton’s laws of motion.

To draw a Free Body Diagram, first choose the body you want to analyse. Then isolate that body mentally from its surroundings and identify every external force acting on it. After that, represent each force by an arrow in the correct direction.

Some common forces shown in an F.B.D. are:

• weight or gravitational force

• normal reaction

• tension

• friction

• applied force

• air resistance, if relevant

Important Point

In Newton’s Third Law, action and reaction forces never appear in the same Free Body Diagram because they act on different objects.

For example, if a book is placed on a table:

• In the F.B.D. of the book, you draw the weight of the book and the normal reaction of the table

• You do not draw the force exerted by the book on the table, because that force acts on the table, not on the book

Impulse and Impulsive Force

Impulse is the total effect of a force acting over a short time interval.

Mathematically, $\vec J = \int \vec F , dt $.

For constant force, $\vec J = \vec F \Delta t $.

Impulse is equal to the change in momentum, so $\vec J = \Delta \vec p = \vec p_f - \vec p_i $.

SI Unit of Impulse

Since impulse equals force multiplied by time, its SI unit is $\text{N s} = \text{kg m s}^{-1} $.

Impulsive Force

A very large force acting for a very short interval of time is called an impulsive force.

Examples:

• hitting a cricket ball with a bat

• hammering a nail

• collision between two vehicles

Why Impulse Matters in Real Life

In many situations, the force may be large, but the contact time decides how much momentum changes.

For example:

• Airbags increase the time of collision, reducing the average force.

• Catching a ball by moving your hands backwards increases the time of impact and reduces the force felt.

Using $F_{\text{avg}} \Delta t = \Delta p $, for the same change in momentum, a larger $\Delta t $means a smaller average force.

Law of Conservation of Linear Momentum

The total linear momentum of an isolated system remains constant if no external force acts on it.

If the net external force is zero, then $\dfrac{d\vec P}{dt} = 0 $.

So, $\vec P = \text{constant} $.

For two bodies before and after interaction, $m_1 \vec u_1 + m_2 \vec u_2 = m_1 \vec v_1 + m_2 \vec v_2 $.

This principle is especially useful in collisions, explosions, and recoil problems.

Applications of Conservation of Momentum

1. Recoil of a gun: Before firing, the total momentum is zero. After firing, if the bullet moves forward, the gun moves backwards so that total momentum remains zero.

If bullet mass is $m $and bullet velocity is $v $, and gun mass is $M $with recoil velocity $V $, then $mv + MV = 0 $.

So, $V = -\frac{mv}{M} $.

2. Rocket propulsion: A rocket moves upward because gases are expelled downward. This is based on momentum conservation along with Newton’s Third Law.

3. Collision problems: Whenever no significant external force acts during the short collision time, momentum conservation can be applied.

Equilibrium of Concurrent Forces

When several forces act on a body, and all of them pass through one point, they are called concurrent forces.

If the body remains at rest or moves with constant velocity, it is in equilibrium.

For equilibrium, the net force must be zero:

• $\sum F_x = 0 $

• $\sum F_y = 0 $

Example of Equilibrium

Suppose a body is hanging by two strings. The tensions in the strings and the weight of the body all act through the same point. These are concurrent forces. To solve such problems, resolve each force into horizontal and vertical components and apply:

• $\sum F_x = 0 $

• $\sum F_y = 0 $

Static Friction and Kinetic Friction

Friction is the force that opposes the relative motion or the tendency of relative motion between two surfaces in contact.

Static Friction

Static friction acts when there is no actual slipping between the surfaces.

It is self-adjusting and takes the value needed to prevent motion, up to a maximum value.

So, $f_s \leq f_{s,\max} $.

The maximum static friction is $f_{s,\max} = \mu_s N $.

Here:

• $\mu_s $is the coefficient of static friction

• $N $is the normal reaction

Key Idea

Static friction is not always equal to $\mu_s N $.

It becomes equal to $\mu_s N $only when the body is just about to move.

This is one of the most common NEET mistakes.

Kinetic Friction

Once the body starts sliding, kinetic friction acts.

Its value is given by $f_k = \mu_k N $.

Usually, $\mu_s > \mu_k $, so kinetic friction is smaller than maximum static friction.

Laws of Friction

The standard laws of dry friction are:

• Friction acts parallel to the surfaces in contact.

• It opposes relative motion or the tendency of motion.

• Limiting friction is proportional to normal reaction, so $f_{\max} = \mu N $.

• For a given pair of surfaces, friction depends on the nature of the surfaces.

• Kinetic friction is generally less than limiting friction.

Angle of Friction

If limiting friction is reached, then $\tan \phi = \mu $, where $\phi $is the angle of friction.

Rolling Friction

Rolling friction is the resistive force that acts when a body rolls over a surface.

It is much smaller than sliding friction. That is why wheels are used in vehicles and luggage bags.

Rolling friction arises because of deformation of the rolling body and the surface.

Example

It is easier to move a suitcase with wheels than to drag it because rolling friction is much less than kinetic friction.

Dynamics of Uniform Circular Motion

When a body moves in a circle with constant speed, its velocity keeps changing because the direction changes continuously.

Hence, even though speed is constant, the body has acceleration. This acceleration is called centripetal acceleration.

Its magnitude is $a_c = \frac{v^2}{r} $.

So the required centripetal force is $F_c = \frac{mv^2}{r} $.

Vehicle on a Level Circular Road

When a vehicle takes a turn on a flat road, the necessary centripetal force is provided by static friction.

So, $f = \dfrac{mv^2}{r} $.

The maximum available static friction is $f_{\max} = \mu_s N = \mu_s mg $.

For safe turning, $\dfrac{mv^2}{r} \leq \mu_s mg $.

So the maximum safe speed is $v_{\max} = \sqrt{\mu_s rg} $.

Vehicle on a Banked Road

On a banked road, the road is tilted so that a component of the normal reaction helps provide the centripetal force.

This reduces dependence on friction and allows safer turning at higher speeds.

If friction is neglected, then the ideal speed for turning on a banked road is given by $\tan \theta = \dfrac{v^2}{rg} $.

So, $v = \sqrt{rg \tan \theta} $.

Here:

• $\theta $is the banking angle

• $r $is the radius of the circular path

• $v $is the speed of the vehicle

Significance

At this speed, the horizontal component of normal reaction provides the exact centripetal force needed, and no friction is required.

When Friction Is Present

If the speed differs from the ideal value, friction acts either up or down the slope depending on whether the vehicle tends to slide down or outward.

For NEET, the frictionless formula $\tan \theta = \dfrac{v^2}{rg} $is the most important result.

Final NEET Revision Points for Laws of Motion

• If the net force is zero, then the acceleration is zero.

• Always draw a correct free-body diagram before writing equations.

• Use $\sum F = ma $for force-based motion problems.

• Use $\Delta p = F \Delta t $or the impulse relation for short-time force interactions.

• Use momentum conservation only when external impulse is negligible.

• Static friction is variable, with $f_s \leq \mu_s N $.

• Kinetic friction is $f_k = \mu_k N $.

• Centripetal force is the net inward force, not an extra force.

• On a level road, friction provides centripetal force.

• On a banked road, the horizontal component of normal reaction helps provide centripetal force.

Overview: Why Laws of Motion are Crucial for NEET

The Laws of Motion unit appears explicitly in the NEET (UG) Physics syllabus (Unit: Laws of Motion) and in CBSE Class 11 Physics.

Key topics covered:

• Force and inertia

• Newton’s laws of motion

• Impulse and conservation of momentum

• Equilibrium of concurrent forces

• Friction: static, kinetic and rolling

• Uniform circular motion: level and banked roads

From a NEET point of view, you can summarise the chapter into two core actions:

1. Draw a correct free‑body diagram (FBD).

2. Apply either Newton’s Second Law in components $\sum F = ma$or momentum conservation for collisions and short‑time interactions.

Common NEET Traps in Laws of Motion

Be careful with these high‑yield mistakes:

• Treating centripetal force as a separate force instead of as the net inward force.

• Thinking action–reaction forces act on the same body (they act on different bodies).

• Assuming static friction = μN in all cases (actually, it is self‑adjusting up to a maximum value).

• Applying momentum conservation when the system experiences a non‑zero external impulse.

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