Class 11 · Chapter 4
Laws of Motion
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
Laws of Motion Short Notes
4 min read
Condensed revision points for Laws of Motion — for quick recall before exams, not a substitute for the full notes.
Newton's Three Laws — Core Statements
- 1st Law: a body stays at rest or moves uniformly unless an external force acts — defines force qualitatively.
- 2nd Law: F = dp/dt; for constant mass, F = ma — measures force.
- 3rd Law: every action has an equal and opposite reaction, acting on two different bodies, simultaneously.
- 1st law is a special case of the 2nd law: F = 0 ⇒ a = 0.
Momentum & Impulse
- Momentum: p = mv (vector, SI unit kg·m/s).
- Impulse: I = F·Δt (constant force) = area under F-t graph (varying force).
- Impulse-momentum theorem: Impulse = Δp.
- Conservation of momentum: if F_net = 0 on a system, total p stays constant.
- Stretching contact time lowers average force for the same Δp (cricketer's hands, shock absorbers, bumpers).
Force Units & Conversions
- 1 kgf = 9.8 N
- 1 gf = 980 dyne
- 1 N = 10^5 dyne
- Unit of force = unit of mass × unit of acceleration.
Apparent Weight in a Lift
- At rest / constant velocity: N = mg
- Accelerating upward: N = m(g + a) → feels heavier
- Accelerating downward: N = m(g − a) → feels lighter
- Free fall (a = g): N = 0 → weightlessness
Connected Bodies, Strings & Pulleys
- Common acceleration: a = F_net / total mass being moved.
- Find 'a' from the whole system first, then isolate one body's FBD for tension/contact force.
- Tension always pulls away from the attachment point; a string can only pull, never push.
- Ideal (massless, frictionless) string/pulley: same tension throughout; pulley only redirects force, doesn't change it.
- Atwood machine: a = (m₁ − m₂)g/(m₁ + m₂); T = 2m₁m₂g/(m₁ + m₂); thrust on pulley R = 2T.
- On an incline + hanging mass: replace mg with mg sinθ for the block on the slope.
Spring Force
- Hooke's law: F = −kx (k = spring constant, N/m).
- Negative sign: force always opposes displacement (restoring force).
- Steady-state spring problems: find force/tension on spring first, then x = F/k.
Pseudo Force (Non-Inertial Frames)
- Inertial frame: at rest or constant velocity — Newton's laws apply directly.
- Non-inertial (accelerating) frame: must add a pseudo force to make Newton's laws work.
- Pseudo force: F = −ma_frame, opposite to the frame's acceleration.
- Pseudo force has no reaction pair — it isn't a real interaction force.
- Pendulum in accelerating train: tan θ = a/g (tilts opposite to acceleration).
Equilibrium of Concurrent Forces
- Translational equilibrium: vector sum of all forces = 0 (no acceleration).
- Two forces in equilibrium: equal magnitude, opposite direction.
- Three forces in equilibrium: form a closed triangle (Lami's theorem).
- Lami's theorem: F₁/sinα = F₂/sinβ = F₃/sinγ (angle opposite each force).
Friction — Key Formulas
- Limiting (max static) friction: f_L = μₛN
- Kinetic friction: f_k = μ_k N (essentially constant once sliding starts).
- μ_k < μₛ always (kinetic friction is slightly less than limiting friction).
- Friction depends on N, not on apparent contact area.
- Angle of friction = angle of repose: tan λ = tan θ = μₛ.
- Acceleration down a rough incline: a = g(sinθ − μ_k cosθ).
- Retardation moving up a rough incline: a = g(sinθ + μ_k cosθ).
Two-Block Friction Systems — Method
- Step 1: Assume blocks move together; find common acceleration aC = F/(total mass).
- Step 2: Find the friction force needed on the unforced block to keep that common acceleration.
- Step 3: Compare to the maximum limiting friction available.
- If required ≤ limiting → move together. If required > limiting → blocks slip; solve each block separately with kinetic friction.
- Pulling > pushing (easier): pulling reduces N, pushing increases N, so pushing always faces more friction.
Common Exam Traps
- Action-reaction pairs never appear together in the same free-body diagram.
- Normal reaction is NOT always equal to mg — only in simple, unaccelerated, no-extra-force cases.
- Pseudo force only appears for an observer INSIDE the accelerating frame, never for a ground/inertial observer.
- Static friction is self-adjusting (varies up to f_L); kinetic friction is constant — don't use μₛ where μ_k is needed.
- Check whether two blocks actually move together before assuming a single common acceleration.
Stuck on a concept in Laws of Motion?
Message Ajay Sir directly on WhatsApp for doubt support on this chapter.