Laws of Motion Class 11 Physics — Revision Notes

TL;DR: Newton's laws of motion describe how objects move and how forces affect their motion, forming the foundation of classical mechanics. These laws explai…

Newton's laws of motion describe how objects move and how forces affect their motion, forming the foundation of classical mechanics. These laws explain eve

Key Points to Remember

• Newton's first law states objects at rest remain at rest and moving objects remain in motion unless acted upon by net force
• Inertia is the property of objects to resist changes in their state of motion
• Mass is a measure of inertia and determines how much force is needed to accelerate an object
• Newton's second law states F = ma, where force equals mass times acceleration
• Net force is the vector sum of all forces acting on an object
• Newton's third law states every action has an equal and opposite reaction force
• Action and reaction forces act on different objects and never cancel each other
• Friction is a force opposing motion between surfaces, depending on normal force and surface properties
• Tension in strings and ropes transmits forces along their length
• Normal force acts perpendicular to surfaces and supports objects against gravity
• Free body diagrams show all forces acting on an object for analysis
• Equations of motion relate initial velocity, final velocity, acceleration, time, and displacement

Important Formulas

• Newton's Second Law: F = ma
• Weight: W = mg (where g = 9.8 m/s²)
• Equations of Motion: v = u + at, s = ut + 1/2 at², v² = u² + 2as
• Friction: f = μN (where μ is coefficient of friction, N is normal force)

Key Terms

• Inertia: Property of objects to resist changes in their state of motion
• Force: Vector quantity that changes an object's velocity or direction
• Acceleration: Rate of change of velocity with respect to time
• Tension: Force transmitted along a string or rope pulling at both ends
• Normal Force: Contact force perpendicular to surfaces supporting objects against gravity
• Free Body Diagram: Representation of an object showing all forces acting on it

Aristotle's fallacy, and why the first law was hard to discover

Aristotle held that an external force is required to keep a body moving with uniform velocity. That matches everyday experience exactly: stop pushing a box and it stops. The law of motion that is actually correct contradicts daily observation, which is why it took nearly two thousand years to state.

The flaw is that the everyday case is never force-free. A moving box on a floor is opposed by friction, so the applied force is not causing the motion — it is cancelling the friction. Remove the friction and no force is needed at all.

Galileo reached this by experiment rather than argument. Rolling a ball down one inclined plane and up another, he observed that the ball rises to nearly the same height regardless of the second plane's slope. As the second plane is made less steep the ball travels further to reach that height. In the limiting case of a horizontal plane it should travel forever, which is the law of inertia.

Why action and reaction never cancel

The third law says that to every action there is always an equal and opposite reaction. Students then ask, reasonably, why anything ever accelerates if every force is cancelled by an equal opposite one.

The resolution is that the two forces act on different bodies. When you push a wall, your force acts on the wall and the wall's force acts on you. Two forces can only cancel when they act on the same body, and these never do.

So when analysing motion, always fix attention on one body, draw only the forces acting on that body, and leave out the reactions it exerts on everything else. That is what a free body diagram is, and it is the single habit that makes these problems tractable. The words action and reaction are also misleading in one respect — there is no cause and effect and no time lag between them; they occur simultaneously.

The three laws, stated precisely

The marks in a board answer come from the exact wording, so learn the statements as given rather than paraphrasing them.

• First law: every body continues in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise. It defines the concept of inertia and identifies when a force is present — namely, whenever the state of motion changes.
• Inertia is the property by which a body resists change in its state, and it is measured by mass. The three forms usually named are inertia of rest, inertia of motion and inertia of direction.
• Second law: the rate of change of momentum of a body is directly proportional to the applied force, and the change takes place in the direction in which the force acts. In symbols, force equals the rate of change of momentum, which reduces to force equals mass times acceleration when the mass is constant.
• Momentum is the product of mass and velocity. It is a vector, its direction is that of the velocity, and its unit is the kilogram metre per second.
• The unit of force follows from the second law: one newton is the force which produces an acceleration of one metre per second squared in a body of mass one kilogram.
• Third law: to every action there is always an equal and opposite reaction. The two forces are of the same nature, act simultaneously, and act on two different bodies, which is why they never cancel each other.

Impulse and conservation of momentum

A large force acting for a very short time is awkward to describe instant by instant, and impulse is the quantity that avoids having to.

• Impulse is the product of force and the time interval for which it acts, and it equals the change in momentum produced. Its unit is the newton second, which is the same as the kilogram metre per second.
• A force that acts for a short duration but produces a finite change in momentum is called an impulsive force — the blow of a bat on a ball, or a collision.
• The impulse-momentum result explains why a cricketer draws the hands back while catching a ball. The change in momentum is fixed by the ball, so lengthening the time of contact reduces the average force on the hands.
• Conservation of momentum follows from the second and third laws together: the total momentum of an isolated system of interacting particles is conserved. Isolated means no net external force acts.
• The standard application is recoil. A gun and bullet initially at rest have zero total momentum, so after firing the momentum of the gun must be equal and opposite to that of the bullet. The gun recoils much more slowly because its mass is far greater.

Friction — static, kinetic and rolling

Friction is a contact force that opposes relative motion, or the tendency to relative motion, between surfaces.

• Static friction is self-adjusting: it takes whatever value is needed to prevent motion, up to a maximum. It is therefore written as less than or equal to the coefficient of static friction times the normal reaction.
• That maximum value is called limiting friction, and it equals the coefficient of static friction multiplied by the normal reaction. A body begins to move the moment the applied force exceeds it.
• Kinetic friction acts once sliding has begun and equals the coefficient of kinetic friction times the normal reaction. It is very nearly independent of the relative speed.
• The coefficient of kinetic friction is less than the coefficient of static friction. This is why a heavy object is harder to start moving than to keep moving.
• Both coefficients are independent of the area of contact, which is the result students find least intuitive. They depend on the nature of the surfaces.
• Rolling friction is much smaller than sliding friction, which is the entire reason for the wheel and for ball bearings in machinery.

Circular motion, level roads and banking

A body in uniform circular motion has a constant speed but a continuously changing velocity, so it is accelerating and a net force must act on it, directed towards the centre.

• The centripetal force needed equals mass times the square of the speed divided by the radius. It is not a new kind of force — some real force must supply it.
• For a car on a level circular road, that force is supplied entirely by static friction between the tyres and the road. The maximum safe speed is therefore the square root of the coefficient of static friction times the radius times the acceleration due to gravity.
• Note what the level-road result does not contain: the mass of the car cancels out. The maximum safe speed is the same for a loaded and an unloaded vehicle on the same road.
• Banking the road tilts the surface so that a component of the normal reaction contributes to the centripetal force, allowing a greater speed without relying wholly on friction.
• On a banked road with friction the maximum speed is the square root of the radius times g times the quantity coefficient of static friction plus the tangent of the banking angle, divided by one minus their product.
• The optimum speed, at which no friction is needed at all, is the square root of the radius times g times the tangent of the banking angle. At this speed the road would be safe even if it were perfectly smooth.

Solved Numericals — Step by Step

Worked Examples

• A passenger lurches forward when a bus brakes — Inertia of motion. The lower body decelerates with the bus, the upper body continues in its state of uniform motion until a force acts on it.
• A cricketer draws the hands back while catching — The change in momentum is fixed, so increasing the contact time reduces the average force. This is the impulse-momentum relation used deliberately.
• A gun recoils when fired — Total momentum before firing is zero, so the momentum of the gun must be equal and opposite to the bullet's. Its far greater mass makes the recoil speed small.
• It is harder to start pushing a crate than to keep it moving — Limiting static friction exceeds kinetic friction, because the coefficient of static friction is greater than the coefficient of kinetic friction.

Common Mistakes Students Make

• Claiming action and reaction cancel each other. They act on two different bodies, and only forces acting on the same body can cancel. This is why a free body diagram must show only the forces on the chosen body.
• Assuming the normal reaction always equals mg. That holds only for a horizontal surface with no vertical component of applied force. On an incline it is mg cos θ, and it changes again if the applied force is at an angle.
• Treating centripetal force as an extra force to be added to a free body diagram. It is the name for the net inward force, supplied by friction, tension, gravity or the normal reaction — never an additional one.
• Writing static friction as μₛN in every case. That is only the maximum value; static friction is self-adjusting and takes whatever value is needed up to that limit.
• Believing friction depends on the area of contact. Both coefficients are independent of the apparent area of contact and depend on the nature of the surfaces.
• Using F = ma when the mass is changing. The second law is properly stated as force equals the rate of change of momentum; F = ma is the special case for constant mass.
• Forgetting that momentum is a vector. In a one-dimensional collision problem, opposite directions must be given opposite signs before applying conservation.

Where This Shows Up in Real Life

Seat belts, airbags and crumple zones

In a collision the change in the passenger's momentum is fixed by the speed of the vehicle, and nothing can alter it. What safety engineering alters is the time over which that change happens. An airbag, a crumple zone and the slight stretch of a seat belt all lengthen the contact time, and since the average force is the change in momentum divided by the time, a longer time means a smaller force on the body. This is the impulse-momentum relation applied directly to saving lives.

Why roads at bends are banked

On a level road the entire centripetal force must come from friction between tyres and road, which fails on a wet or worn surface. Banking tilts the road so that a component of the normal reaction points towards the centre of the curve and contributes to the centripetal force. At the optimum speed no friction is required at all, so the bend remains safe even in rain. This is why highways and railway tracks are banked at curves, with the angle chosen for the expected speed.

Rocket propulsion

A rocket works purely by the third law and conservation of momentum. Hot gases are expelled backwards at high speed, and the rocket gains an equal and opposite momentum forwards. It needs nothing to push against, which is why rockets work in the vacuum of space where an aircraft engine could not. The rocket's mass changes continuously as fuel burns, which is exactly the case where the second law must be used in its momentum form rather than as F = ma.

Friction as both problem and necessity

Friction wastes energy in machinery and wears parts out, so it is reduced by lubricants, ball bearings and polished surfaces — replacing sliding friction with the much smaller rolling friction. Yet without friction walking would be impossible, since the forward push on a person comes from the reaction to the backward push of the foot on the ground, and no vehicle could start or stop. The engineering question is never how to eliminate friction but where to increase it and where to reduce it.

Board-Style Questions with Model Answers

State Newton's second law of motion and derive the relation F = ma from it. (3 marks)

The law states that the rate of change of momentum of a body is directly proportional to the applied force, and the change takes place in the direction in which the force acts. Momentum p equals mv, so the rate of change of momentum is the derivative of mv with respect to time. If the mass is constant it comes out of the derivative, leaving m times the derivative of v with respect to time, which is m times acceleration. Introducing the constant of proportionality and choosing the unit of force so that the constant is one, we obtain F = ma. The derivation assumes constant mass, so for a system of changing mass such as a rocket the law must be used in its momentum form.

Why do action and reaction not cancel each other even though they are equal and opposite? (2 marks)

Because the two forces act on two different bodies. For two forces to cancel and produce no acceleration they must act on the same body, and an action-reaction pair never does. When a person pushes a wall, the force of the person acts on the wall while the reaction of the wall acts on the person, so each body experiences only one of the two forces. This is also why a free body diagram must include only the forces acting on the chosen body.

Derive an expression for the maximum speed of a car on a level circular road of radius r. (3 marks)

For circular motion the net inward force must equal mv² divided by r. On a level road the only horizontal force available is static friction between the tyres and the road, whose maximum value is μₛ times the normal reaction. On a level road the normal reaction equals mg, so the maximum friction is μₛmg. Setting mv² divided by r equal to μₛmg and cancelling the mass from both sides gives v² = μₛrg, so the maximum speed is the square root of μₛrg. The mass cancels, which means the maximum safe speed does not depend on how heavily the car is loaded.

Define impulse and show that it equals the change in momentum. Explain why a cricketer moves his hands backwards while catching a ball. (5 marks)

Impulse is defined as the product of the force and the time interval for which it acts. By the second law the force equals the rate of change of momentum, so force multiplied by time interval equals the change in momentum, which establishes the result. Its unit is the newton second, equivalent to the kilogram metre per second. When catching a ball the cricketer must reduce its momentum to zero, and that change in momentum is fixed by the mass and speed of the ball and cannot be altered. Since the change in momentum equals the average force multiplied by the contact time, drawing the hands back increases the contact time and therefore reduces the average force experienced by the hands, which prevents injury.

State the law of conservation of momentum and apply it to the recoil of a gun. (3 marks)

The law states that the total momentum of an isolated system of interacting particles is conserved, where isolated means that no net external force acts on the system. Before firing, the gun and bullet are both at rest, so the total momentum of the system is zero. No net external horizontal force acts during firing, so the total momentum after firing must also be zero. Therefore the momentum of the gun must be equal in magnitude and opposite in direction to that of the bullet. Since the mass of the gun is much greater than that of the bullet, its recoil velocity is correspondingly much smaller.

Explain why the first law of motion is not obvious from everyday experience. (3 marks)

Everyday experience suggests Aristotle's view, that a force is needed to keep a body moving uniformly, because a moving object on a surface always slows down and stops when the push is removed. The reason is that everyday motion is never free of opposing forces: friction and air resistance act continuously. The applied force in such cases is not producing the motion but merely balancing these resistive forces. Galileo's inclined plane experiments showed that as the opposing influence is reduced the body travels further, and in the limiting case of no opposing force it would continue indefinitely, which is the first law.

Assertion–Reason Questions (CBSE Format)

For each question choose: (a) both A and R are true and R is the correct explanation of A; (b) both are true but R is not the correct explanation; (c) A is true but R is false; (d) A is false but R is true.

Quick Self-Check

Key Terms Glossary

Inertia

The property of a body by which it resists any change in its state of rest or of uniform motion; it is measured by mass.

Momentum

The product of mass and velocity of a body; a vector quantity with unit kilogram metre per second.

Newton

The SI unit of force; the force that produces an acceleration of one metre per second squared in a mass of one kilogram.

Impulse

The product of a force and the time interval for which it acts; it is equal to the change in momentum produced.

Impulsive force

A force that acts for a very short duration but produces a finite change in momentum, as in a collision.

Free body diagram

A diagram showing only the forces acting on one chosen body, used to apply the second law to that body.

Normal reaction

The contact force exerted by a surface on a body, directed perpendicular to the surface.

Limiting friction

The maximum value that static friction can attain, equal to the coefficient of static friction times the normal reaction.

Kinetic friction

The friction acting once sliding has begun, equal to the coefficient of kinetic friction times the normal reaction.

Rolling friction

The resistance encountered when a body rolls over a surface; much smaller than sliding friction.

Centripetal force

The net force directed towards the centre of a circular path, of magnitude mv² divided by r; supplied by a real force, never an extra one.

Banking of roads

Raising the outer edge of a curved road so that a component of the normal reaction helps provide the centripetal force.

Equilibrium of a particle

The condition in which the net external force on the particle is zero, so it remains at rest or moves with uniform velocity.

One-Minute Revision

• Aristotle was wrong because everyday motion is never friction-free; the applied force cancels friction rather than causing the motion.
• First law defines inertia and tells you when a force is present. Mass is the measure of inertia.
• Second law properly: force equals rate of change of momentum. F = ma only when mass is constant.
• Third law: equal, opposite, simultaneous, same nature — and on DIFFERENT bodies, which is why nothing cancels.
• Impulse = force × time = change in momentum. Lengthen the time to cut the force — airbags, catching a ball.
• Momentum is conserved when no net external force acts. Gun and bullet start at zero, so they end at zero.
• Static friction is self-adjusting; μₛN is only its maximum. Kinetic friction is smaller, so starting is harder than continuing.
• Friction does not depend on the area of contact — only on the nature of the surfaces.
• Level road: v_max = √(μₛ r g), and the mass cancels out.
• Banked road optimum speed: v = √(r g tan θ), needing no friction at all.

Syllabus reference: NCERT Class 11 Physics — Laws of Motion. Assumes the kinematics of Motion in a Straight Line and Motion in a Plane, and feeds directly into Work, Energy and Power and System of Particles.

Frequently Asked Questions

What does Newton's first law mean?

Newton's first law states that objects at rest stay at rest and moving objects maintain constant velocity unless a net force acts on them. This is the law of inertia

How does F = ma explain everyday motion?

F = ma shows that the same force produces different accelerations depending on mass. A light object accelerates more than a heavy object under the same force

Why don't action and reaction forces cancel?

Action and reaction forces act on different objects, so they cannot cancel each other. They are equal in magnitude but opposite in direction, affecting different bodies

Is centripetal force a separate force acting on a body?

No, and treating it as one is the most common error in this chapter. Centripetal force is simply the name given to the net force directed towards the centre of the circular path. In each situation it is supplied by an ordinary force already present: friction for a car on a level road, tension for a stone whirled on a string, gravity for a satellite, and a component of the normal reaction on a banked road. It should never be drawn as an extra arrow on a free body diagram alongside the force that actually provides it.

Why does friction not depend on the area of contact?

Because what matters is the actual microscopic contact between the surfaces rather than the apparent area. When the apparent area is increased the same weight is spread over more of it, so the pressure at each point falls and the true contact area stays roughly the same. The result is that the frictional force depends on the normal reaction and the nature of the two surfaces, but not on how large the surfaces appear to be.

When should I use F = ma and when the momentum form of the second law?

Use F = ma whenever the mass of the body is constant, which covers almost every problem in this chapter. Use the momentum form, that force equals the rate of change of momentum, whenever the mass changes during the motion. The standard case is a rocket, which loses mass continuously as it burns fuel, and problems involving a falling chain or a conveyor belt being loaded. The momentum form is the general statement and F = ma is a special case of it.

Does the maximum safe speed on a bend change when the car is fully loaded?

On a level road it does not. Equating the required centripetal force mv²/r to the maximum friction μₛmg allows the mass to cancel, leaving v² = μₛrg, which contains no mass term. The same cancellation occurs in the banked-road expressions. In practice a heavily loaded vehicle handles differently for other reasons, such as a raised centre of gravity making it more likely to topple before it skids, but the skidding speed predicted by this analysis is unchanged.

More Class 11 Physics Revision Notes

• Units and Measurements
• Laws of Motion
• Units and Measurements

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