Laws of Motion Class 11 Physics Quick Recall Sheet (Short Notes 2026-27)

Mechanics Visual: Dynamics, Forces, and Friction

[!TIP] 🚀 2-Minute Quick Recall Summary (Save for Exam Day)

1st Law: Inertia (object resists change in motion).

2nd Law: F = ma; Force = rate of change of momentum (dp/dt).

3rd Law: Action = Reaction (on different bodies).

Banking of Roads: v_max = √[rg (μ + tanθ)/(1 - μ tanθ)].

Friction: f_s ≤ μ_s N; f_k = μ_k N. Friction always opposes relative motion. 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

If Kinematics is the "What" of motion, Dynamics is the "Why." Newton's Laws of Motion are the foundation upon which the entire edifice of Classical Mechanics stands. They allow us to predict the trajectory of objects ranging from a pebble on the beach to the motion of celestial bodies. This chapter transitions from describing motion to identifying its causes: Forces. These "Comprehensive" revision notes provide exhaustive theoretical depth, including the proof that Newton's Second Law is the "Real Law," the derivation of the Banking of Roads, and advanced Free Body Diagram (FBD) strategies for competitive exams like JEE and NEET.

1. Newton's Three Laws: The Principles of Force

I. First Law (Law of Inertia)

Theorem: An object remains in its state of rest or uniform motion unless acted upon by an external unbalanced force.

Inertia: The inherent property of matter that resists change.
Types: Inertia of Rest, Motion, and Direction.

II. Second Law (The Law of Dynamics)

Derivation: The rate of change of momentum is directly proportional to the applied force.

Momentum (p) = mv.
F ∝ dp/dt => F = k (dp/dt).
Substituting p = mv: F = d(mv)/dt.
If mass is constant: F = m (dv/dt) = ma. Conclusion: F = ma is the mathematical consequence of the Second Law.

III. Third Law (Action-Reaction)

Theorem: For every action, there is an equal and opposite reaction.

Key Note: Action and reaction never act on the same body; therefore, they never cancel each other out.

2. Proof: The Second Law is the "Real Law"

Proof:

Second Law contains First Law: If F = 0, then ma = 0 => a = 0. This means the object stays at rest or in uniform motion (First Law).
Second Law contains Third Law: By using the conservation of momentum (derived from F = dp/dt) for an isolated system, we can prove that F_ab = -F_ba.

3. Impulse and Momentum

Impulse (J): A large force acting for a very short duration. Derivation (Impulse-Momentum Theorem):

F = dp/dt.
∫ F dt = ∫ dp.
J = Δp = p_final - p_initial. Conclusion: Impulse is numerically equal to the change in momentum.

4. Equilibrium of Forces & Lami’s Theorem

When multiple forces act on a particle such that the net force is zero, the particle is in equilibrium. Lami’s Theorem: For three concurrent forces in equilibrium: P / sinα = Q / sinβ = R / sinγ (where α, β, γ are the angles opposite to forces P, Q, R).

5. The Physics of Friction

Friction is a self-adjusting contact force that opposes relative motion.

Static Friction (fs) ≤ μs N. (Self-adjusting up to a limit).
Kinetic Friction (fk) = μk N. (Constant once motion starts).
Angle of Friction (θ): tanθ = μ.

6. Circular Dynamics: Banking of Roads

When a vehicle takes a turn, it needs centripetal force. On a flat road, this is provided solely by friction (v_max = √μrg). To increase safety, roads are "banked" (tilted).

Derivation: Maximum Velocity on a Banked Road

Consider a vehicle of mass m on a road banked at angle θ with coefficient of friction μ.

Vertical Equation: N cosθ = mg + f sinθ.
Horizontal Equation (Centripetal): N sinθ + f cosθ = mv² / r.
Substitute f = μN and solve for v:
- v_max = √[ rg (μ + tanθ) / (1 - μ tanθ) ].

[!TIP] Optimum Velocity: If friction is zero (icy road), the safe speed is v = √rg tanθ.

Comprehensive Exam Strategy (Q&A)

Q1: Why is it easier to pull a lawnmower than to push it? Answer: When you push, a component of your force acts downward, increasing the Normal reaction (N = mg + F sinθ), which increases friction. When you pull, a component acts upward, decreasing the Normal reaction (N = mg - F sinθ), thereby reducing friction.

Q2: Can a single force exist in nature? Answer: No. Forces always exist in pairs (Newton’s Third Law). Even if we analyze one body, there is an equal and opposite force acting on the other.

Q3: A man jumps from a height. Why does he bend his knees upon landing? Answer: By bending his knees, he increases the time of impact (Δt). Since F = Δp / Δt, a larger time interval reduces the impact force felt by his legs, preventing injury.

Related Revision Notes

Conclusion

Newton’s Laws of Motion provide the fundamental rules of the game of Physics. From the simple friction between our shoes and the ground to the complex banking of high-speed racing tracks, these principles govern every interaction in the physical world. Master the derivation of the Banking of Roads and the logic of Impulse, and you will find that the most complex mechanics problems resolve into simple balances of force. Stay balanced, stay in motion, and remember: Every action counts!

Reference: MIT OpenCourseWare: Newton’s Laws