Laws of Motion – Newton’s Laws, Forces & Friction | Complete Notes for Engineering Entrance Exams

LAWS OF MOTION — SHORT NOTES (Entrance Exam Focus)

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1. Newton’s First Law (Law of Inertia)

A body continues in its state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.

Types of Inertia

1. Inertia of rest

2. Inertia of motion

3. Inertia of direction

If net force = 0 → acceleration = 0.

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2. Newton’s Second Law (F = ma)

Rate of change of momentum is directly proportional to the applied force and occurs in the direction of the force.

$$F=\frac{dp}{dt}=ma$$

Key Points

• Defines force quantitatively.

• SI unit: Newton (N).

• If mass constant → F ∝ a.

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3. Newton’s Third Law (Action–Reaction)

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

• Action and reaction act on different bodies.

• They occur simultaneously.

• They never cancel each other.

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4. Linear Momentum

$$p=mv$$

• Vector quantity

• Conserved if net external force = 0.

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5. Impulse

$$\text{Impulse}=F\cdot \mathrm{\Delta }t=\mathrm{\Delta }p$$

Large change in momentum in a short time.
Used in: batting, airbags, cushioning.

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6. Free Body Diagram (FBD)

A diagram showing all forces acting on a body.

Common forces:

• Weight: ( mg )

• Normal reaction: ( N )

• Tension: ( T )

• Applied force: ( F )

• Friction: ( f )

• Spring force: ( kx )

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7. Equilibrium of Forces

• Static Equilibrium: net force = 0, net torque = 0

• Dynamic Equilibrium: moving with constant velocity

$$\sum F_x = 0,\qquad \sum F_y = 0$$

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8. Friction

Opposes relative motion.

Types

1. Static friction

$$f_s\le {\mu }_{s}N$$

2. Kinetic friction:

$$f_k={\mu }_{k}N$$

2. Rolling friction: very small

3. Limiting friction: maximum static friction

Observation

$${\mu }_s>{\mu }_k$$

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9. Angle of Repose

Angle at which body just begins to slide down an inclined plane.

$$\tan\theta = \frac{f_s}{N} = \mu_s$$

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10. Motion on Inclined Plane

Component of weight

• Parallel to plane: $mg\sin\theta$
  

• Perpendicular to plane: $mg\cos\theta$
  

Acceleration on smooth incline

$$a=g\sin \theta$$

On rough incline

$$a=g(\sin \theta -\mu \cos \theta )$$

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11. Tension in a String

For a mass $m$ hanging:

$$T=mg$$

If accelerating upward:

$$T=m(g+a)$$

If accelerating downward:

$$T=m(g-a)$$

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12. Pulley Systems (Important for Exams)

1. Atwood’s Machine

Two masses $m_1, m_2$ on either side of a pulley.

Acceleration:

$$a=\frac{m_2-m_1}{m_2+m_1}g$$

Tension:

$$T=\frac{2m_1{m}_2}{m_1+m_2}g$$

2. One mass on table, one hanging

$$a = \frac{mg}{m + M}$$

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13. Contact Forces

When two bodies touch → normal reaction + friction arise.

Normal Reaction:

• Acts perpendicular to surface.

• Not always = mg (depends on motion).

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14. Pseudo Force (non-inertial frame)

If a system accelerates with a, a pseudo force acts on mass m inside it:

$$F_p=ma$$

Direction: opposite to acceleration of the frame.

Used in lift problems, accelerating cars.

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15. Common Exam Mistakes

• Confusing action–reaction with equilibrium forces

• Assuming N = mg always

• Forgetting friction direction

• Wrong FBD for pulleys

• Missing pseudo force in accelerating frames

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16. Most Expected Numerical Types

1. Block on incline (smooth/rough)

2. Pulley systems (Atwood, double pulleys)

3. Lift problems (apparent weight)

4. Truck/car accelerating → block inside

5. Friction limiting case

6. Connected bodies on horizontal plane

7. Action–reaction identification