Newton's Laws of Motion (NLM)

Concept Map

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1. Basic Concepts

flowchart LR
    A["Basic Concepts"]
    A --> B1["1. Inertia
Resistance to change in state of rest or uniform motion"]
    A --> B2["2. Mass
$$m$$ — measure of inertia (SI: kg)"]
    A --> B3["3. Force
$$F$$ — interaction that changes motion (SI: N)"]
    A --> B4["5. Inertia in different situations
Rest, uniform motion, rotational motion"]
    A --> B5["10. Free Body Diagram (FBD)"]
    A --> B6["11. Types of forces
Contact and non-contact"]
    A --> B7["30. Centre of Mass
System behaves as a single particle for translation"]
    A --> B8["57. Frames of Reference
Inertial and non-inertial"]
    A --> B9["58. Fictitious / Pseudo Force
$$F = m\omega^2 r$$"]
    

2. Newton's Laws

flowchart LR
    A["Newton's Laws"]
    A --> L1["4. First Law
$$\sum F = 0$$
Body remains at rest or in uniform straight-line motion"]
    A --> L2["6. Second Law
$$F = \frac{dp}{dt}$$"]
    A --> L3["7. Constant Mass
$$F = ma$$"]
    A --> L4["8. Third Law
Action and reaction are equal and opposite"]
    A --> L5["9. Principle of Superposition
$$\vec{F} = \vec{F}_1 + \vec{F}_2 + \dots$$"]
    A --> L6["28. Pseudo Force
$$F_p = -ma$$"]
    A --> L7["29. Equilibrium
Translation: sum F = 0
Rotation: sum tau = 0"]
    

3. Forces

flowchart LR
    A["Forces"]
    A --> F1["12. Gravitational Force
$$F = G\frac{m_1m_2}{r^2}$$"]
    A --> F2["13. Weight
$$W = mg \approx 9.8\,\mathrm{m/s^2}$$"]
    A --> F3["14. Normal Reaction
$$N$$ — perpendicular to surface"]
    A --> F4["15. Tension
$$T$$ — force transmitted through a string"]
    A --> F5["31. Constraint Forces
Normal reaction, tension, etc."]
    A --> F6["32. Ideal Pulley
Tension is the same on both sides for an ideal string and pulley"]
    

4. Friction

 
flowchart LR 
    A["Friction"] 
    A --> FR1["16. Frictional Force
Static: fs ≤ μs N
Kinetic: fk = μk N"] 
    A --> FR2["17. Limiting Friction
$$f_{max} = \mu_s N$$"] 
    A --> FR3["18. Angle of Repose
$$\tan\theta = \mu_s$$"] 
    A --> FR4["19. Kinetic Friction
Usually $$\mu_k \lt \mu_s$$"] 
    A --> FR5["20. Rolling Friction
Usually much smaller than sliding friction"] 
    A --> FR6["41. Coefficient of Friction
$$\mu$$ is dimensionless"] 
    A --> FR7["42. Friction Coefficients
Usually $$\mu_s \gt \mu_k$$"] 
    A --> FR8["43. Factors Affecting Friction
Nature of surfaces and normal reaction"] 
    A --> FR9["44. Work Done by Friction
For opposing friction: $$W = -fs$$"] 
    

5. Applications

flowchart LR
    A["Applications"]
    A --> A1["21. Friction on Incline
For impending/sliding: $$f = \mu mg\cos\theta$$ (N = mg cos θ)"]
    A --> A2["22. Condition for Sliding
Inclined plane: $$\tan\theta > \mu_s$$"]
    A --> A3["23. Rough Horizontal Surface
$$a = \frac{F - \mu_k mg}{m}$$"]
    A --> A4["24. Vertical String
Accelerating mass: $$T = m(g \pm a)$$"]
    A --> A5["25. Atwood's Machine
$$a = \frac{(m_2 - m_1)g}{m_1 + m_2}$$"]
    A --> A6["26. Elevator
$$N = m(g \pm a)$$"]
    A --> A7["27. Apparent Weight
Normal force on weighing scale"]
    A --> A8["33. Smooth Incline
$$a = g\sin\theta$$ (down the plane)"]
    A --> A9["34. Rough Incline
$$a = g(\sin\theta - \mu_k\cos\theta)$$"]
    A --> A10["35. Block with Applied Force
$$a = \frac{F - \mu_k mg}{m}$$"]
    A --> A11["36. Two Blocks in Contact
Common acceleration + Newton's laws"]
    

6. Circular Motion

flowchart LR
    A["Circular Motion"]
    A --> C1["37. Centripetal Force
$$F_c = \frac{mv^2}{r}$$"]
    A --> C2["38. Banked Road without Friction
$$\tan\theta = \frac{v^2}{rg}$$"]
    A --> C3["39. Vertical Circular Motion
Top: N + mg = mv²/r
Bottom: N - mg = mv²/r"]
    A --> C4["40. Conical Pendulum
T cosθ = mg ; T sinθ = mv²/r"]
    A --> C5["59. Rough Circular Path
Friction can provide the required centripetal force"]
    

7. Momentum, Impulse & Collisions

flowchart LR
    A["Momentum and Collisions"]
    A --> W1["45. Instantaneous Power
$$P = Fv\cos\theta$$"]
    A --> W2["46. Impulse
For constant force: $$J = F\Delta t = \Delta p$$"]
    A --> W3["47. Momentum
$$p = mv$$"]
    A --> W4["48. Conservation of Momentum
Valid when net external force is zero"]
    A --> W5["49. Elastic Collision
Momentum and kinetic energy are conserved"]
    A --> W6["50. Inelastic Collision
Momentum is conserved in isolated system"]
    A --> W7["51. Perfectly Inelastic Collision
Bodies stick together"]
    A --> W8["52. Coefficient of Restitution
$$e = \frac{v_2-v_1}{u_1-u_2}$$ for 1D convention"]
    A --> W9["53. Range of Restitution Coefficient
$$0 \le e \le 1$$ for passive collisions"]
    A --> W10["54. Explosion
Momentum conserved in isolated system"]
    A --> W11["55. Rocket Propulsion
Variable-mass system"]
    A --> W12["56. Variable-Mass Equation
$$F = m\frac{dv}{dt} + v\frac{dm}{dt}$$ under 1D convention"]
    

8. Constants & Key Takeaways

flowchart TD
    A["Constants and Key Takeaways"]
    A --> K1["60. Important Constants
G ≈ 6.67×10⁻¹¹ N m²/kg²
g ≈ 9.8 m/s²"]
    A --> K2["Key Takeaways
Draw clear free-body diagrams
Identify all forces and their directions
Use momentum conservation for isolated systems
Apply circular-motion equations correctly
Check assumptions, signs and limiting cases"]
    

Newton's Laws of Motion
Flowcharts rendered using Mermaid and KaTeX

Yogendra Gopal Borse

Civil Engineer | Assistant Engineer Grade-I, Maharashtra PWD

B.Tech (Civil) from VJTI Mumbai. Experienced in bridge design, road works, estimation, project monitoring and digital engineering tools. Creator of YogiPWD – practical technical resources for civil engineers.

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