Newton’s Laws of Motion Class 11: All Formulas & Formula Sheet with Free PDF Download (Physics, JEE & NEET)
Newton's Laws of Motion Formula Sheet — Competishun
Newton's Laws of Motion Class 11: All Formulas & Formula Sheet with Free PDF Download (Physics, JEE & NEET)
Newton's Laws of Motion are the backbone of all of classical mechanics. Every time you solve a force problem, draw a free body diagram or calculate tension in a string, you are using these three laws. They are not just important for Class 11. They are the foundation that every mechanics chapter in JEE and NEET builds on.
This page gives you the complete Newton's Laws of Motion formula sheet for Class 11 in one place. It covers all three laws, linear momentum and impulse, free body diagrams, friction (static and kinetic), angle of friction, motion on an inclined plane, pseudo force, connected bodies and the Atwood machine, with worked examples. Grab the free PDF below and keep it handy for revision.
Download the Newton's Laws of Motion Formula Sheet PDF
Get all three laws, friction, pseudo force, Atwood machine and connected body formulas in one clean PDF, free. Perfect for Class 11, JEE and NEET revision.
Download Free PDFWhat Are Newton's Laws of Motion?
Newton's Laws of Motion are three fundamental rules published by Sir Isaac Newton in 1687 that describe how forces affect the motion of objects. Together they form the complete foundation of classical mechanics and they appear in JEE Main, JEE Advanced and NEET every single year without exception.
Here is what the Laws of Motion chapter covers and what this formula sheet includes:
Newton's Three Laws of Motion
First Law — Law of Inertia
An object at rest stays at rest and an object moving at constant velocity keeps moving at that velocity unless a net external force acts on it.
Inertia is the tendency of an object to resist any change in its state of motion. Greater mass means greater inertia. A book sitting on a table, passengers jolted forward when a bus brakes suddenly, a ball rolling on a frictionless floor — all of these are examples of the first law in everyday life.
Second Law — Law of Acceleration
The net force acting on an object equals its rate of change of momentum.
Here F is in Newtons, m in kilograms, a in m/s squared and p is linear momentum in kg m/s. The general form F = dp/dt works even when mass changes with time, which is why it is used in variable mass problems in JEE Advanced.
Third Law — Law of Action and Reaction
For every action force there is an equal and opposite reaction force, and these two forces always act on different bodies.
A foot pushing the ground backward, the ground pushing the foot forward. A rocket pushing exhaust gas downward, the gas pushing the rocket upward. The key point is that action and reaction always act on different objects, so they never cancel each other in any single free body diagram.
Linear Momentum and Impulse
| Concept | Formula | Note |
|---|---|---|
| Linear momentum | p = mv | Vector quantity; unit kg·m/s |
| Newton's 2nd law (general) | F = dp/dt | Works for variable mass too |
| Impulse | J = F · Δt = Δp | Unit N·s = kg·m/s |
| Impulse–momentum theorem | F · Δt = m(v − u) | Force × time = change in momentum |
| Conservation of momentum | If Fnet = 0, then p = constant | Used in all collision problems |
| Impulse equals the area under a Force vs time graph. | ||
Free Body Diagram — How to Draw One
A Free Body Diagram shows all the forces acting on a single object, with that object isolated from everything else around it. It is the most important problem-solving tool in this entire chapter. If your FBD is wrong, your answer will be wrong.
- Isolate the object: Draw only the object you are analysing, nothing else.
- Show weight: W = mg acting downward, always present.
- Show normal force: N acting perpendicular to the surface, pointing away from it.
- Show applied forces: Tension, push or pull forces in the direction they act.
- Show friction: Always parallel to the surface and opposing relative motion or the tendency of motion.
- Apply F = ma: Resolve forces along your chosen axes and write the equations.
Friction — All Formulas
Friction is the force that opposes relative motion or the tendency of relative motion between two surfaces in contact. It is one of the most heavily tested topics in Laws of Motion questions across JEE and NEET.
| Type / Concept | Formula | Note |
|---|---|---|
| Static friction (maximum) | fs ≤ μs N | Adjusts itself up to the maximum value |
| Kinetic (sliding) friction | fk = μk N | Constant once sliding begins |
| Relation between coefficients | μk < μs | Easier to keep sliding than to start |
| Normal force (flat surface) | N = mg | When there is no vertical acceleration |
| Normal force (inclined plane) | N = mg cos θ | Where θ is the angle of the incline |
| Friction on inclined plane | f = μ mg cos θ | Acts up the slope when block slides down |
| Angle of friction (λ) | tan λ = μs | Angle between resultant contact force and normal |
| Angle of repose (θr) | tan θr = μs | Maximum slope angle before the block starts sliding |
| Condition for sliding on incline | tan θ > μs | Block slides when incline angle exceeds repose angle |
| Friction always acts parallel to the surface, opposing relative motion or the tendency of motion. | ||
Motion on an Inclined Plane
| Situation | Acceleration |
|---|---|
| Smooth incline (no friction) | a = g sin θ |
| Rough incline, block sliding down | a = g(sin θ − μk cos θ) |
| Rough incline, block pushed up | a = g(sin θ + μk cos θ) |
| Condition for the block not to slide | tan θ ≤ μs |
Pseudo Force — Non-Inertial Frames
When you solve a problem from inside an accelerating reference frame such as a lift, a car or a train, Newton's laws do not directly apply. To use F = ma in such a frame, you add a pseudo force to all objects in the frame.
The pseudo force is not a real force. It has no Newton's third law reaction pair. It is a mathematical tool that makes calculations easier when you choose to work from an accelerating frame.
| Situation | Pseudo Force Direction | Apparent Weight |
|---|---|---|
| Lift accelerating upward | Downward | N = m(g + a) |
| Lift accelerating downward | Upward | N = m(g − a) |
| Lift in free fall (a = g) | Upward, equal to mg | N = 0 (weightlessness) |
| Car accelerating forward | Backward | Passenger feels pushed back into seat |
| Pseudo force = −m·a₀. No real reaction pair. Only valid inside non-inertial frames. | ||
Connected Bodies and the Atwood Machine
Two Blocks on a Horizontal Surface
Masses m1 and m2 connected by a string on a smooth surface, with force F applied on m1:
Atwood Machine (Two Masses Over a Pulley)
Masses m1 and m2 hanging over a frictionless, massless pulley with m1 greater than m2:
| Quantity | Formula |
|---|---|
| Acceleration | a = (m1 − m2)g / (m1 + m2) |
| Tension in string | T = 2m1m2g / (m1 + m2) |
| Reaction force on pulley | R = 2T = 4m1m2g / (m1 + m2) |
Block on Table Connected to Hanging Mass
Mass m1 on a smooth horizontal table connected via a string over a pulley to hanging mass m2:
All Formulas at a Glance
| Formula | What It Means |
|---|---|
| Fnet = ma | Net force equals mass times acceleration |
| F = dp/dt | Force equals rate of change of momentum |
| p = mv | Linear momentum |
| J = F·Δt = Δp | Impulse equals change in momentum |
| fs ≤ μsN | Static friction (up to its maximum value) |
| fk = μkN | Kinetic friction (constant while sliding) |
| tan λ = μs | Angle of friction equals angle of repose |
| N = mg cos θ | Normal force on an inclined surface |
| a = g sin θ | Acceleration on a smooth inclined plane |
| a = g(sin θ − μ cos θ) | Acceleration down a rough inclined plane |
| Fpseudo = −ma0 | Pseudo force in a non-inertial reference frame |
| N = m(g ± a) | Apparent weight in an accelerating lift |
| a = (m1−m2)g / (m1+m2) | Atwood machine acceleration |
| T = 2m1m2g / (m1+m2) | Atwood machine string tension |
Worked Examples
| Problem | Solution |
|---|---|
| Force needed to give a 5 kg block an acceleration of 3 m/s² | F = ma = 5 × 3 = 15 N |
| Maximum static friction: mu = 0.4, m = 10 kg | f = μN = 0.4 × 100 = 40 N |
| Angle of repose when mu = 0.5 | θ = arctan(0.5) = 26.6° |
| Atwood machine: m₁ = 6 kg, m₂ = 4 kg | a = (6−4)×10/10 = 2 m/s² and T = 2×6×4×10/10 = 48 N |
| Apparent weight in a lift: m = 70 kg, a = 2 m/s² upward | N = 70 × (10 + 2) = 840 N |
| Impulse from a force of 20 N applied for 0.5 seconds | J = 20 × 0.5 = 10 N·s |
Common Mistakes to Avoid
- Cancelling action and reaction in one FBD: They act on different bodies and can never cancel each other in a single free body diagram.
- Using the wrong normal force on inclines: On a slope, N = mg cos θ, not mg. This mistake leads to wrong friction values.
- Confusing static and kinetic friction: Static friction adjusts itself and can be less than μsN. Kinetic friction is always exactly μkN once sliding starts.
- Forgetting the pseudo force: Solving a problem from an accelerating frame without adding the pseudo force gives the wrong acceleration.
- Getting tension wrong in connected systems: Find the system acceleration first, then isolate each body to solve for tension.
- Misreading the first law: Zero net force means zero acceleration, not zero velocity. The object can still be moving.
Why Newton's Laws Matter for JEE and NEET
- Very high weightage: Laws of Motion appears in every JEE Main, JEE Advanced and NEET paper, typically contributing three to five questions per exam.
- Foundation for every mechanics chapter: Work and Energy, Rotational Motion, Gravitation and Fluid Mechanics all depend on a solid understanding of Newton's laws.
- FBD skill applies everywhere: Once you can draw correct FBDs confidently, every force problem in physics becomes structured and solvable.
- Friction is a standalone scoring topic: Static friction, kinetic friction and angle of repose each appear as direct questions. Knowing the formulas is not enough; you need to know when to apply which.
- Quick to score once you practise: The concept load in this chapter is manageable. Consistent practice with numericals converts understanding into reliable marks fast.
How to Use This Formula Sheet
- Understand each law before memorising: Read the statement of each law and convince yourself it makes physical sense before looking at the formulas.
- Practise drawing FBDs every day: Take any force problem, close the solution, and draw the FBD yourself first. This is the skill that separates average scores from high scores.
- Memorise the friction formulas: Static friction, kinetic friction and angle of repose appear directly in questions. These must be at the tip of your fingers.
- Derive the Atwood machine results yourself: JEE Advanced likes derivation-style questions. Know where the formula comes from, not just the answer.
- Skim the PDF before every test: A two-minute glance at this sheet before a mock refreshes all the key values and prevents avoidable mistakes under time pressure.
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Frequently Asked Questions — Newton's Laws of Motion
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