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Laws of Motion and Forces — NDA Physics

Laws of Motion is one of NDA Physics's most reliably-tested chapters — roughly 44 PYQs across 2018–2026, almost entirely EASY and MODERATE (only ~10% HARD). The chapter teaches in five progressive movements: (1) Types of forces — fundamental vs contact, conservative vs non-conservative, and the equilibrium types; the vocabulary the rest of the chapter assumes; (2) Newton's three laws — inertia, F = ma, action-reaction, plus combining forces into a resultant (the chapter's single HARD-heavy idea); (3) Impulse and momentum — p = mv, impulse = change in momentum, and the cushioning principle (why a fielder pulls his hands back); (4) Conservation of momentum and collisions — recoil, the rate-of-change-of-mass force, and equal-mass elastic collisions; (5) Friction — f = μN, the static > kinetic > rolling ordering, and stopping a moving block. Most marks come from one-line recall and a single F = ma / p = mv substitution — drill the formula, drill the trap, walk out with the marks.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

All 44 past questions NDA Physics strategy NDA home All formulas on one page

Subtopic notes

Formula & revision sheet

13 formulas · 5 reference tables · 19 gotchas across all subtopics — the exam-eve cheat-sheet

Types of Forces — the Vocabulary of the Chapter

Formulas (1)

What a force is — the foundation · Definition of the newton (from Newton's second law) $1\,\text{N} = 1\,\text{kg} \cdot 1\,\text{m s}^{-2}$

Reference tables (3)

Fundamental forces vs contact forces5 rows

Force	Type	Range / note
Gravitational	Fundamental, non-contact	Always attractive; infinite range; weakest of the four
Electromagnetic	Fundamental, non-contact	Source of friction, tension, normal, contact forces at large scale
Strong nuclear	Fundamental	Binds protons and neutrons in the nucleus; very short range
Weak nuclear	Fundamental	Responsible for radioactive (beta) decay; very short range
Friction / Normal / Tension	Contact (derived)	Need physical contact; obey Newton's third law; can act solid-fluid NDA 2024 — contact forces (1) need contact, (2) obey the third law, (3) can act between a solid and a fluid: all three statements are correct.

The four fundamentals are the only true forces; everyday contact forces are electromagnetic in origin. NDA tests "which are fundamental?" (answer: all of gravity, EM, and the two nuclear forces).

Conservative vs non-conservative forces; central forces5 rows

Force	Conservative?	Central?
Gravitational	Conservative	Central
Electrostatic	Conservative	Central
Spring (elastic restoring)	Conservative	Central (along the spring)
Friction	Non-conservative	Non-central NDA 2019 — the force that is BOTH non-central AND non-conservative is friction (electric and gravitational are central and conservative).
Air resistance / viscous drag	Non-conservative	Non-central

Friction is the only common force that is simultaneously non-central and non-conservative — a frequent NDA distractor target.

Equilibrium and restoring forces3 rows

Type	Response to small push	Example
Stable	Returns to original position	Ball at the bottom of a bowl; pendulum bob
Unstable	Moves further away	Ball balanced on top of a vertical rod NDA 2018 — a ball balanced on a vertical rod is in UNSTABLE equilibrium.
Neutral	Stays in the new position	Ball resting on a flat horizontal table

Restoring force is the signature of stable equilibrium; for a pendulum, gravity supplies it (NDA 2018).

Watch out for (3)

Force is a vector — direction matters
→ What a force is — the foundation
Friction is a contact force; magnetism is non-contact — ALWAYS
→ Fundamental forces vs contact forces
Gravity acts as the RESTORING force for a pendulum
→ Equilibrium and restoring forces

Newton's Three Laws of Motion

Formulas (5)

First law — inertia · Condition for the first law (equilibrium of motion) $\vec{F}_{\text{net}} = 0 \iff \vec{a} = 0$
Second law — F = ma · Newton's second law $\vec{F} = \frac{d\vec{p}}{dt} = m\vec{a} \quad (\text{constant } m)$
Third law — action and reaction · Newton's third law (force pair) $\vec{F}_{AB} = -\vec{F}_{BA}$
Combining forces — the parallelogram law · Magnitude of the resultant of two forces $R = \sqrt{P^2 + Q^2 + 2PQ\cos\theta}$
Rotational inertia — moment of inertia of common bodies · Moment of inertia of common bodies (mass M, radius R) $I_{\text{ring}} = MR^2, \quad I_{\text{disc}} = \tfrac{1}{2}MR^2, \quad I_{\text{sphere}} = \tfrac{2}{5}MR^2$

Reference tables (1)

Mass vs weight5 rows

Property	Mass	Weight
What it is	Amount of matter / inertia	Gravitational force on the body
Formula	—	W = mg
SI unit	kilogram (kg)	newton (N)
Scalar or vector	Scalar	Vector (downward)
Varies with location?	No — same everywhere	Yes — changes with g NDA 2018 — mass is "the same everywhere"; NDA 2021 — mass is the constant of proportionality in F = ma.

Mass is constant and is the proportionality constant in F = ma; weight = mg varies with g. NDA tests both halves of this distinction.

Watch out for (8)

Constant velocity does NOT mean changing speed
→ First law — inertia
Force is proportional to rate of change of momentum, NOT to momentum itself
→ Second law — F = ma
Watch the units when computing F = ma
→ Second law — F = ma
Action-reaction pairs act on DIFFERENT bodies
→ Third law — action and reaction
Two equal forces with a resultant equal to each: θ = 120°
→ Combining forces — the parallelogram law
Don't add force magnitudes arithmetically
→ Combining forces — the parallelogram law
Mass is the constant of proportionality, NOT weight
→ Mass vs weight
Same mass + radius, different I — distribution decides
→ Rotational inertia — moment of inertia of common bodies

Impulse and Momentum

Formulas (2)

Linear momentum, p = mv · Linear momentum $\vec{p} = m\vec{v}$
Impulse = change in momentum; the cushioning principle · Impulse-momentum theorem $J = F\,\Delta t = \Delta p = m(v - u)$

Watch out for (3)

On an elastic bounce, momentum changes but speed and KE don't
→ Linear momentum, p = mv
Cushioning increases TIME to reduce FORCE
→ Impulse = change in momentum; the cushioning principle
Net force on the floor in a bounce includes weight
→ Impulse = change in momentum; the cushioning principle

Conservation of Momentum and Collisions

Formulas (3)

Conservation of linear momentum · Conservation of momentum (two bodies) $m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2$
Force when mass is added or ejected (variable mass) · Force to maintain speed while loading mass at rate dm/dt $F = v\,\frac{dm}{dt}$
Collisions — elastic and the equal-mass result · Equal-mass elastic head-on collision (m₂ initially at rest) $v_1' = 0, \qquad v_2' = u_1$

Watch out for (4)

Internal forces can't move the centre of mass
→ Conservation of linear momentum
Vertically-falling mass adds no horizontal momentum
→ Force when mass is added or ejected (variable mass)
Equal-mass elastic collision: velocities are EXCHANGED
→ Collisions — elastic and the equal-mass result
Use momentum (not KE) to find the unknown speed
→ Collisions — elastic and the equal-mass result

Friction

Formulas (2)

Limiting (maximum) friction, f = μN · Limiting friction $f_{\max} = \mu N$
Friction as the only horizontal force — stopping a block · Friction from stopping (work-energy form) $f \, s = \tfrac{1}{2} m u^2 \;\Rightarrow\; f = \frac{m u^2}{2s}$

Reference tables (1)

Static, kinetic, and rolling friction3 rows

Type	When it acts	Relative size
Static	Before sliding starts	Largest (up to μ_s N)
Kinetic / sliding	While the body slides	Intermediate (μ_k N)
Rolling	While the body rolls	Smallest NDA 2024 — the correct ordering is Static friction > Kinetic friction > Rolling friction.

Rolling friction is the smallest, which is why wheels and ball bearings reduce resistance. NDA tests the ordering directly.

Watch out for (1)

Use the correct normal force, not always mg
→ Limiting (maximum) friction, f = μN

PYQ weightage by concept

18 concepts · 44 PYQs — where the marks actually sit, so you know what to drill first

Types of Forces — the Vocabulary of the Chapter6 PYQs · 14%

Concept	PYQs	Share
Fundamental forces vs contact forces	3	7%
Equilibrium and restoring forces	2	5%
Conservative vs non-conservative forces; central forces	1	2%
What a force is — the foundationfoundation	—	—

Newton's Three Laws of Motion20 PYQs · 45%

Concept	PYQs	Share
First law — inertia	6	14%
Second law — F = ma	5	11%
Combining forces — the parallelogram law	4	9%
Mass vs weight	2	5%
Rotational inertia — moment of inertia of common bodies	2	5%
Third law — action and reaction	1	2%

Impulse and Momentum6 PYQs · 14%

Concept	PYQs	Share
Impulse = change in momentum; the cushioning principle	5	11%
Linear momentum, p = mv	1	2%

Conservation of Momentum and Collisions9 PYQs · 20%

Concept	PYQs	Share
Conservation of linear momentum	5	11%
Force when mass is added or ejected (variable mass)	2	5%
Collisions — elastic and the equal-mass result	2	5%

Friction3 PYQs · 7%

Concept	PYQs	Share
Limiting (maximum) friction, f = μN	1	2%
Friction as the only horizontal force — stopping a block	1	2%
Static, kinetic, and rolling friction	1	2%

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