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Laws of Motion

NCERT Class 11 Physics Chapter 4

Laws of Motion for Class 11 Physics, JEE and NEET: Newton’s laws, inertia, momentum and impulse, equilibrium, friction, circular motion and banking.

10 topics Updated 8 Nov 2026

For: Class 11, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus, NEET Class 11 syllabus

With your textbook

NCERT Physics Part I (Class 11), Chapter 4 “Laws of Motion”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.1 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Aristotle’s fallacy

    Why uniform motion needs no net force, how friction misleads us, with solved examples and practice questions.

    Class 11 only NCERT Section 4.2 11 min read 3 solved examples 4 practice questions

  2. The law of inertia

    Galileo’s inclined planes, inertia of rest, motion and direction, mass as its measure, and solved examples.

    NCERT Section 4.3 14 min read 3 solved examples 7 practice questions

  3. Newton’s first law of motion

    Statement, meaning, inertial frames, examples and common mistakes.

    NCERT Section 4.4 9 min read 3 solved examples 3 practice questions

  4. Newton’s second law of motion

    F = dp/dt and F = ma derived, impulse, SI unit of force, 3 solved examples and practice.

    NCERT Section 4.5 13 min read 3 solved examples 8 practice questions

  5. Newton’s third law of motion

    Action and reaction forces, why they never cancel, recoil and other examples, and practice.

    NCERT Section 4.6 9 min read 3 solved examples 3 practice questions

  6. Conservation of momentum

    Derivation from Newton’s laws, recoil of a gun, collisions and explosions, with solved examples.

    NCERT Section 4.7 14 min read 3 solved examples 7 practice questions

  7. Equilibrium of a particle

    Concurrent forces, resolving into components, triangle of forces and Lami’s theorem, with examples.

    NCERT Section 4.8 12 min read 3 solved examples 7 practice questions

  8. Friction and other common forces

    Static and kinetic friction, the coefficient of friction, laws of friction, angle of repose and rolling friction.

    NCERT Section 4.9 19 min read 3 solved examples 8 practice questions

  9. Dynamics of circular motion

    Mv/R, the highest safe speed on a level road, the banking of roads derivation and solved examples.

    NCERT Section 4.10 15 min read 3 solved examples 8 practice questions

  10. Solving problems in mechanics

    Choosing the system, the step-by-step method, blocks in contact, the Atwood machine and connected bodies.

    NCERT Section 4.11 14 min read 3 solved examples 7 practice questions

Key formulas in this chapter

Aristotle’s fallacy

  • Fnet = 0 in uniform motion
  • F = f (steady pull against friction)
  • a = −f/m (slowing down once the pull stops)

Law of inertia

  • Fnet = 0 means v is constant (law of inertia)
  • a = Fnet/m, so a1/a2 = m2/m1 for the same force
  • a = g sin θ along a smooth incline
  • v = √(2gh) at the foot of a smooth incline of height h
  • L = h/sin θ (path up a smooth incline to regain height h)

Newton’s first law

  • Fnet = 0 means v is constant
  • a = 0 when Fnet = 0

Newton’s second law

  • F = dp/dt
  • F = ma (constant mass)
  • 1 N = 1 kg m s
  • J = Favg Δt = Δp
  • N = m(g + a) in a lift accelerating up
  • N = m(g − a) in a lift accelerating down

Newton’s third law

  • FAB = −FBA
  • a = F/m for each body
  • M V = m v (recoil, both start at rest)

Conservation of momentum

  • P = constant when Fext = 0
  • mu + mu = mv + mv
  • V = −mv/M (recoil, both at rest before firing)
  • v = (mu + mu)/(m + m) when the bodies stick together
  • Kgun/Kbullet = m/M

Equilibrium of a particle

  • ΣF = 0 (equilibrium of a particle)
  • ΣFx = 0, ΣFy = 0, ΣFz = 0
  • F + F + F = 0 (three forces: a closed triangle)
  • F/sin α = F/sin β = F/sin γ (Lami’s theorem)
  • Fx = F cos θ, Fy = F sin θ

Friction

  • fs ≤ μs N (static friction)
  • fk = μk N (kinetic friction), μk < μs
  • F = −kx (spring force)
  • tan θ = μs (angle of repose)
  • a = g(sin θ − μk cos θ) (sliding down a rough incline)
  • a = g(sin θ + μk cos θ) (deceleration sliding up)
  • amax = μs g (box on an accelerating floor)

Dynamics of circular motion

  • fc = mv2/R = mω2R
  • vmax = √(μs R g) (level road)
  • vo = √(R g tan θ) (banked road, no friction)
  • vmax^2 = R g (μs + tan θ) / (1 − μs tan θ) (banked road)
  • vmin^2 = R g (tan θ − μs) / (1 + μs tan θ) (banked road)
  • tan θ = v2/(R g) (banking angle at which speed v needs no friction)

Solving problems in mechanics

  • ΣFx = m ax and ΣFy = m ay for each body
  • a = F/(m1 + m2) (two bodies pushed or pulled together on a smooth surface)
  • a = (m1 − m2)g/(m1 + m2) (Atwood machine)
  • T = 2m1m2g/(m1 + m2) (Atwood machine)
  • a = (m2g − μk m1g)/(m1 + m2) (block on a table pulled by a hanging block, while m2 moves down; starting from rest requires m2 > μs m1)

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