Newton’s Laws of Motion, Friction and Momentum Conservation

Why does a passenger jerk forward when a bus suddenly brakes? Why does a gun recoil when fired? How does a rocket fly in space where there is no air to push against? All these everyday puzzles are answered by the three laws of motion given by Sir Isaac Newton. While kinematics describes how objects move, the laws of motion – part of dynamics – explain why they move, by connecting motion with force.

Laws of motion, friction and momentum are among the most frequently asked Physics topics in SSC CGL, CHSL, MTS, GD, RRB NTPC, Group D, ALP, JE, WBCS, Police, Defence and State PSC exams. Questions come on inertia and its examples, force and its units, momentum and impulse, action–reaction pairs, conservation of momentum, types of friction, apparent weight in a lift and circular motion. This guide explains everything in simple language with diagrams, formulas, solved examples, memory tricks and 20 MCQs with answers.

➤ Newton's laws: Published in Principia Mathematica (1687)
➤ First law: Law of inertia – a body stays at rest or in uniform motion unless an external force acts
➤ Second law: F = ma = rate of change of momentum · SI unit of force: newton (N)
➤ Third law: Every action has an equal and opposite reaction – acting on different bodies
➤ Momentum: p = mv · Conserved when no external force acts (gun recoil, rocket)
➤ Friction order: Static (limiting) > Kinetic (sliding) > Rolling · μ = f / N (no unit)
➤ Lift: Apparent weight more when accelerating up, less when accelerating down, zero in free fall

What is Force?

A force is a push or a pull that can change the state of rest or motion of an object, change its speed or direction, or change its shape. Force is a vector quantity. Its SI unit is the newton (N): 1 N is the force that gives a mass of 1 kg an acceleration of 1 m/s². In the CGS system the unit is the dyne (1 N = 10⁵ dyne). The gravitational unit is the kilogram-force: 1 kgf = 9.8 N.

Fundamental forces of nature (strongest to weakest): strong nuclear force → electromagnetic force → weak nuclear force → gravitational force. Gravity is the weakest, but it has infinite range and holds planets and galaxies together.

Newton's First Law – Law of Inertia

Statement: An object remains at rest, or continues to move in a straight line with uniform velocity, unless an external unbalanced force acts on it.

This tendency of an object to resist any change in its state of rest or motion is called inertia. Galileo Galilei first understood inertia through his experiments with balls rolling on inclined planes; Newton turned it into a law. Mass is the measure of inertia – a heavier object has more inertia and is harder to start, stop or turn. That is why it is harder to push a loaded truck than a bicycle.

Seat belts in cars protect passengers by stopping their forward motion due to inertia during sudden braking.

Momentum

Momentum (p) is the "quantity of motion" of a body, equal to the product of its mass and velocity: p = m × v. It is a vector quantity with SI unit kg·m/s (also written N·s). A slow-moving truck and a fast-moving bullet can both have large momentum – the truck because of its big mass, the bullet because of its high velocity.

Example: A cricket ball of mass 0.15 kg moving at 40 m/s has momentum p = 0.15 × 40 = 6 kg·m/s.

Newton's Second Law – Force and Acceleration

Statement: The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.

F = Δp / Δt = m (v − u) / t = m × a

The second law tells us how much a body accelerates for a given force. Doubling the force doubles the acceleration; doubling the mass halves it. The first law is actually a special case of the second law – if F = 0, then a = 0 and velocity does not change.

Example 1: A force acts on a 5 kg body and produces an acceleration of 2 m/s². Force = ma = 5 × 2 = 10 N.

Impulse – Large Force for a Short Time

When a large force acts for a very short time (as in hitting, kicking or a collision), we use impulse: Impulse = F × t = change in momentum (Δp). Its unit is N·s. For the same change in momentum, increasing the time of impact reduces the force. This simple idea explains many safety designs:

Example 2: A 0.2 kg ball hits a wall at 10 m/s and bounces back at 10 m/s. The contact lasts 0.02 s. Change in momentum = 0.2 × [10 − (−10)] = 4 kg·m/s. Average force = 4 ÷ 0.02 = 200 N.

Newton's Third Law – Action and Reaction

Statement: To every action, there is an equal and opposite reaction.

Forces always come in pairs. When body A pushes body B, B pushes A back with an equal force in the opposite direction. The most important point: action and reaction act on two different bodies, so they never cancel each other.

Law of Conservation of Momentum

Statement: If no external force acts on a system, the total momentum of the system remains constant. Momentum before = momentum after.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

This law follows from Newton's second and third laws. Its most famous example is the recoil of a gun (Figure 1). Before firing, the gun and bullet are at rest, so total momentum = 0. After firing, the bullet moves forward and the gun moves backward so that the total momentum is still zero.

Figure 1: Recoil of a gun – the forward momentum of the bullet equals the backward momentum of the gun

Example 3: A 5 kg gun fires a 20 g (0.02 kg) bullet at 500 m/s. Recoil velocity V = m v / M = 0.02 × 500 / 5 = 2 m/s backward. Because the gun is much heavier, it moves much more slowly than the bullet – yet a soldier must hold it firmly against the shoulder.

Rockets: A rocket works on the conservation of momentum (and the third law). It throws hot gases backward at very high speed, and gains an equal forward momentum. It does not need air to push against, so it works even in the vacuum of space. ISRO launches its rockets from the Satish Dhawan Space Centre, Sriharikota.

Friction

Friction is the force that opposes the relative motion (or attempted motion) between two surfaces in contact. It acts parallel to the surfaces and opposite to the direction of motion. It arises mainly because of the tiny irregularities (roughness) of surfaces that interlock with each other.

Types of Friction

Order: Static (limiting) friction > Kinetic friction > Rolling friction. That is why it is easier to keep a heavy box moving than to start it, and why wheels were such a great invention. Figure 2 shows how friction changes as the applied force increases.

Figure 2: Friction versus applied force – static friction grows up to a limiting value, then kinetic friction (slightly less) acts once the body starts sliding

Laws and Formula of Friction

Limiting friction is directly proportional to the normal reaction (N) – the force with which the surface pushes back on the body (equal to its weight mg on a horizontal surface):

f = μ N where μ = coefficient of friction (a pure number with no unit)

• Friction depends on the nature (roughness) of the surfaces and the normal force.
• Friction is nearly independent of the area of contact.
• Angle of repose: On an inclined plane, the angle at which a body just begins to slide down satisfies tan θ = μ (Figure 3).

Example 4: A 10 kg box rests on a floor with μ = 0.4. Taking g = 10 m/s², limiting friction = μmg = 0.4 × 10 × 10 = 40 N. A push of more than 40 N is needed to move it.

Figure 3: Free-body diagram of a block on an inclined plane – weight acts downward, normal reaction perpendicular to the surface, and friction up the slope

Friction – A Necessary Evil

Apparent Weight in a Lift

The reading on a weighing machine is the normal reaction (N) of the floor, called apparent weight. In a lift, it changes with the lift's acceleration (a):

Example 5: A 60 kg person stands in a lift accelerating upward at 2 m/s² (g = 10 m/s²). Apparent weight = 60 × (10 + 2) = 720 N. If the lift accelerates downward at 2 m/s², it becomes 60 × 8 = 480 N. Astronauts in an orbiting spacecraft feel weightless because they and their craft are continuously falling freely around the Earth.

Dynamics of Circular Motion

An object moving in a circle needs a force directed towards the centre, called the centripetal force: F = m v² / r. Without it, the object would fly off along a straight line (tangent) because of inertia.

Banking of roads: On curved roads and railway tracks, the outer edge is raised above the inner edge so that vehicles can turn safely at higher speed without depending only on friction. The ideal banking angle is given by tan θ = v² / rg. A cyclist leans inward while turning for the same reason. The outward "centrifugal force" felt by passengers is a pseudo (fictitious) force seen from the rotating frame; a washing-machine dryer and a cream separator work on this principle.

Example 6: A 1000 kg car takes a turn of radius 50 m at 20 m/s. Centripetal force = mv²/r = 1000 × 400 / 50 = 8,000 N.

Laws of Motion – Formula Sheet

West Bengal Connection – Forces in Kolkata's Landmarks

Kolkata's famous bridges are lessons in balanced forces. The Howrah Bridge (Rabindra Setu), opened in 1943, is a balanced cantilever bridge built without nuts and bolts – its steel parts are riveted together. The huge weight of the bridge and its traffic is balanced by equal and opposite reaction forces from its two main towers and foundations, a direct example of equilibrium and Newton's third law. The Vidyasagar Setu, opened in 1992, is a cable-stayed bridge in which the tension in steel cables balances the weight of the deck. Kolkata's trams and metro also show inertia in action – standing passengers sway forward when the vehicle brakes and backward when it starts.

Continue your physics revision with Light Reflection and Refraction, and read how ISRO's rockets inspire students in Darbhanga Planetarium's ISRO Space Gallery. For other science topics, see Carbon and Organic Chemistry and Climatology (where the Coriolis force deflects winds). Practise with the CSIR NAL MTS Mock Test.

20 MCQs on Laws of Motion

Q1. Newton's first law of motion is also called the law of:
(a) Momentum
(b) Inertia
(c) Action and reaction
(d) Gravitation

Answer: (b) – A body continues in its state of rest or uniform motion unless an external force acts on it.

Q2. The measure of inertia of a body is its:
(a) Mass
(b) Velocity
(c) Weight
(d) Volume

Answer: (a) – Greater mass means greater inertia.

Q3. Passengers fall forward when a moving bus stops suddenly. This is due to:
(a) Inertia of rest
(b) Inertia of direction
(c) Inertia of motion
(d) Friction

Answer: (c) – The bus stops, but the upper body tends to keep moving forward.

Q4. Dust comes out of a carpet when it is beaten with a stick because of:
(a) Inertia of motion
(b) Third law of motion
(c) Friction
(d) Inertia of rest

Answer: (d) – The carpet moves suddenly, but the dust particles tend to remain at rest and fall off.

Q5. The SI unit of force is:
(a) Newton
(b) Joule
(c) Dyne
(d) Watt

Answer: (a) – 1 N = 1 kg·m/s²; the dyne is the CGS unit (1 N = 10⁵ dyne).

Q6. What force is needed to give a 4 kg body an acceleration of 3 m/s²?
(a) 7 N
(b) 1.33 N
(c) 12 N
(d) 0.75 N

Answer: (c) – F = ma = 4 × 3 = 12 N.

Q7. Momentum of a body is the product of its:
(a) Mass and acceleration
(b) Mass and velocity
(c) Force and time
(d) Weight and height

Answer: (b) – p = mv; force × time is impulse.

Q8. A cricketer moves his hands backward while catching a fast ball to:
(a) Increase the force on hands
(b) Increase the momentum of the ball
(c) Reduce the momentum change
(d) Increase the time of impact and reduce the force

Answer: (d) – Impulse F × t = Δp is fixed, so a longer time means a smaller force on the hands.

Q9. Impulse is equal to:
(a) Change in momentum
(b) Change in kinetic energy
(c) Mass × acceleration
(d) Force × distance

Answer: (a) – Impulse = F × t = Δp; force × distance is work.

Q10. Action and reaction forces do not cancel each other because they:
(a) Are unequal
(b) Act in the same direction
(c) Act on different bodies
(d) Act at different times

Answer: (c) – They are equal and opposite but act on two different bodies.

Q11. The working of a rocket is based on:
(a) Newton's first law
(b) Conservation of energy only
(c) Bernoulli's principle
(d) Newton's third law and conservation of momentum

Answer: (d) – Gases pushed backward produce a forward thrust; it works even in vacuum.

Q12. A 4 kg gun fires a 10 g bullet at 400 m/s. The recoil velocity of the gun is:
(a) 1 m/s
(b) 4 m/s
(c) 0.1 m/s
(d) 10 m/s

Answer: (a) – V = mv/M = 0.01 × 400 / 4 = 1 m/s, opposite to the bullet.

Q13. The law of conservation of momentum holds when:
(a) Friction is maximum
(b) No external force acts on the system
(c) Kinetic energy is conserved
(d) Bodies are at rest

Answer: (b) – Total momentum stays constant in an isolated system.

Q14. Which of the following is the smallest?
(a) Static friction
(b) Limiting friction
(c) Rolling friction
(d) Sliding friction

Answer: (c) – Rolling friction is much smaller than sliding friction, which is why wheels and ball bearings are used.

Q15. The coefficient of friction (μ) has:
(a) Unit of newton
(b) Unit of joule
(c) Unit of N/m
(d) No unit

Answer: (d) – μ = f/N is a ratio of two forces.

Q16. Ball bearings are used in machines to:
(a) Convert sliding friction into rolling friction
(b) Increase friction
(c) Increase the weight
(d) Produce heat

Answer: (a) – Rolling friction is much less than sliding friction.

Q17. A man in a lift feels heavier when the lift:
(a) Moves down with uniform velocity
(b) Accelerates downward
(c) Accelerates upward
(d) Falls freely

Answer: (c) – Apparent weight = m(g + a); in free fall it becomes zero.

Q18. Astronauts in an orbiting spacecraft feel weightless because:
(a) There is no gravity in space
(b) Their mass becomes zero
(c) The spacecraft is very large
(d) They and the spacecraft are in free fall

Answer: (d) – Gravity still acts and provides the centripetal force for the orbit; both fall freely together, so the normal reaction is zero.

Q19. Roads are banked on curves to:
(a) Provide the necessary centripetal force
(b) Increase friction
(c) Reduce the speed of vehicles
(d) Drain rainwater only

Answer: (a) – A component of the normal reaction supplies centripetal force; ideal angle tan θ = v²/rg.

Q20. The Howrah Bridge (Rabindra Setu) in Kolkata is a:
(a) Suspension bridge
(b) Balanced cantilever bridge
(c) Cable-stayed bridge
(d) Arch bridge

Answer: (b) – Opened in 1943, it is built without nuts and bolts; the Vidyasagar Setu is a cable-stayed bridge.

Want more practice? Try our Daily GK Quiz and Mock Tests.

Conclusion

Newton's three laws explain why things move the way they do – inertia keeps bodies in their state, force changes momentum, and every action has an equal and opposite reaction. Conservation of momentum explains gun recoil and rockets, while friction – a necessary evil – lets us walk and drive but also wastes energy. For exams, remember the statements of the three laws with everyday examples, the formulas F = ma, p = mv, impulse = F × t, f = μN, apparent weight in a lift and centripetal force, and the order of friction. Revise the tricks above and practise the MCQs regularly.

Reference: NCERT Science Class IX ("Force and Laws of Motion"); NCERT Science Class VIII ("Friction"); NCERT Physics Class XI ("Laws of Motion").