What is the formula for centripetal force?

The centripetal force is F = mv²/r = mω²r, directed toward the centre of the circle. It is not a new force — it is supplied by a real force such as tension, gravity, friction or the normal force.

Laws of Motion Class 11 Notes — Formulas, Key Concepts & FAQ

Q: Is Laws of Motion important for NEET and JEE?

Yes. Laws of Motion is a high-weightage Class 11 Physics chapter that usually contributes 1–2 questions in both NEET and JEE, and it is the foundation for work–energy, rotation and gravitation.

Q: What is the difference between mass and weight?

Mass is the amount of matter in a body (a scalar measured in kilograms) and is the measure of inertia. Weight is the gravitational force on the body, W = mg (a vector measured in newtons), and it changes with the value of g.

Q: Why do action and reaction forces not cancel out?

Because the action and reaction forces act on two different bodies. Only forces acting on the same body can be added together or cancelled on its free-body diagram.

Q: How can I revise Laws of Motion quickly before an exam?

Use the 5-minute quick-revision points, memorise the Formula Handbook, then attempt this chapter's previous-year questions (PYQs) and review only the ones you got wrong.

Laws of Motion is the chapter that explains why an object speeds up, slows down or changes direction. It rests on Newton's three laws and three ideas — inertia, momentum and force — and it is one of the highest-weightage Class 11 Physics chapters in both NEET and JEE. Master it and the rest of mechanics (work–energy, rotation, gravitation) becomes far easier.

Chapter snapshot


Class / Subject	Class 11 · Physics
Exams	NEET, JEE (Main & Advanced), CUET, IISER
Typical weightage	~3–5% of the paper (regularly 1–2 questions)
Prerequisites	Motion in a straight line & in a plane (vectors)
Difficulty	Moderate — conceptual, high scoring with practice

What will you learn?

State and apply Newton's three laws of motion.
Define inertia, linear momentum and impulse and use them.
Draw and solve free-body diagrams (FBDs) for connected bodies.
Handle friction (static vs kinetic) and motion on an incline.
Find the centripetal force needed for uniform circular motion.

5-minute quick revision

Net force zero ⇒ no acceleration (first law); non-zero ⇒ a = F_net / m.
F = dp/dt, and for constant mass F = ma (second law).
Forces come in equal, opposite pairs on different bodies (third law).
Momentum is conserved when no external force acts: Σp = constant.
Friction: f_s ≤ μ_s N (a range), f_k = μ_k N (once sliding).
Circular motion needs a net inward force F_c = mv²/r — supplied by a real force.

What are Newton's three laws of motion?

First law (law of inertia). A body stays at rest, or in uniform straight-line motion, unless a net external force acts on it. It defines force qualitatively and introduces the inertial frame. Inertia is the tendency to resist a change in motion, and mass is its measure.

Second law. The rate of change of momentum is proportional to the applied force and is in its direction: F = dp/dt. For constant mass this is the familiar F = ma. One newton is the force that gives a 1 kg mass an acceleration of 1 m/s².

Third law. To every action there is an equal and opposite reaction. The two forces are equal in magnitude, opposite in direction, and act on two different bodies — which is exactly why they never cancel each other.

Key concepts: momentum and impulse

Linear momentum p = mv is a vector (SI unit kg·m/s) — the "quantity of motion".
Impulse J = F·Δt = Δp. A large force acting for a short time (a bat hitting a ball) produces a finite change in momentum. On an F–t graph, impulse is the area under the curve.
Conservation of momentum: with no net external force, total momentum is constant. This underlies collisions, recoil of a gun and rocket propulsion.

How do you draw a free-body diagram?

Isolate one body, draw every force acting on it — weight mg (down), normal N, tension T, the applied force, and friction f — then apply ΣF = ma along chosen axes. For connected bodies, find the acceleration from the whole system first, then the tension from a single body's FBD. A correct FBD solves most problems instantly.

Friction — static vs kinetic

Static friction adjusts itself to prevent motion, up to a maximum f_s(max) = μ_s N. It is a range 0 ≤ f_s ≤ μ_s N, not a fixed value.
Kinetic friction f_k = μ_k N acts once sliding begins, and usually μ_k < μ_s.
Friction always opposes the relative motion (or its tendency).
On an incline, a block is on the verge of slipping when tan θ = μ_s (the angle of repose).

Uniform circular motion

A body moving in a circle of radius r needs a net inward (centripetal) force F_c = mv²/r = mω²r. This is not a new force — gravity, tension, the normal force or friction provides it. The so-called "centrifugal force" only appears in a rotating (non-inertial) frame and is a pseudo-force.

High-weightage topics for NEET & JEE

Free-body diagrams of connected blocks (pulleys, lifts).
Friction on horizontal surfaces and inclines (angle of repose).
Conservation of momentum (collisions, recoil).
Apparent weight in a lift (N = m(g ± a)).
Centripetal force and the maximum speed on a flat/banked road.

Common mistakes & exam traps

Treating an action–reaction pair as acting on the same body (they don't, so they can't cancel on one FBD).
Forgetting that static friction is a range, not always μ_s N.
Assuming N = mg always — in a lift, on an incline, or with a vertical applied component, it isn't.
Mixing up μ_s and μ_k, or switching between g = 9.8 and 10 m/s² within a problem.
Calling the centripetal force an "extra" force instead of naming the real force that supplies it.

Topper tips

Spend the first 30 seconds of every problem drawing a clean FBD — speed comes from the diagram, not from memorising special cases.
Write ΣF = ma per axis; solve the system, then back-substitute for tension or normal force.
Check units and signs (negative marking punishes a dropped minus more than a missed question).

PYQ trend analysis

Across recent NEET and JEE papers, this chapter reliably contributes 1–2 questions, most often on friction/incline, connected-body FBDs and momentum conservation. JEE (Advanced) tends to combine it with work–energy or rotation, so practise multi-concept problems once the basics are firm.

Smart revision strategy

Read these notes, then the Formula Handbook.
Practise this chapter's previous-year questions (PYQs) under timed conditions.
Re-attempt only the questions you got wrong after re-reading the relevant concept — that single loop fixes most score leaks.

Frequently asked questions

Is Laws of Motion important for NEET and JEE? Yes. It is a high-weightage Class 11 chapter that usually contributes 1–2 questions in both exams and is the foundation for work–energy, rotation and gravitation.

What is the difference between mass and weight? Mass is the amount of matter in a body (a scalar, in kg) and measures inertia; weight is the gravitational force on it, W = mg (a vector, in newtons), which changes with g.

Why do action and reaction forces not cancel out? Because they act on two different bodies. Only forces acting on the same body can be added or cancelled on its free-body diagram.

What is the centripetal force formula? F_c = mv²/r = mω²r, directed toward the centre of the circle. It is supplied by a real force such as tension, gravity, friction or the normal force.

How can I revise Laws of Motion quickly before an exam? Use the 5-minute quick-revision list above, memorise the Formula Handbook, then attempt this chapter's previous-year questions (PYQs) and review only your mistakes.

Laws of Motion — Revision Notes