Laws of Motion
'Nature and Nature's laws lay hid in night. God said, Let Newton be! and all was light.' — Alexander Pope
1. Chapter Overview
Kinematics tells us HOW objects move. DYNAMICS tells us WHY they move the way they do. The answer lies in Newton's THREE LAWS of motion — the CORNERSTONE of classical mechanics. This chapter covers Newton's laws, the concept of INERTIA, MOMENTUM, IMPULSE, FRICTION, and the dynamics of CIRCULAR MOTION.
2. Newton's First Law of Motion (Law of Inertia)
- Statement: An object at rest stays at rest, and an object in motion stays in motion with the SAME speed and direction, UNLESS acted upon by an UNBALANCED external force.
- Inertia: The TENDENCY of an object to resist change in its state of motion
- Inertia of Rest: Difficulty starting motion (person jerked backward when bus starts)
- Inertia of Motion: Difficulty stopping (person thrown forward when bus stops suddenly)
- Inertia of Direction: Difficulty changing direction (passenger leans sideways in a turning car)
- Mass is the MEASURE of inertia — larger mass = larger inertia
Galileo's Thought Experiment
A ball rolling down one incline will roll up the opposite incline to NEARLY the same height. As the opposite incline is flattened, the ball travels farther to reach that height. On a perfectly flat surface, it would roll FOREVER (idealised, no friction).
3. Newton's Second Law of Motion
- Statement: The rate of change of momentum of an object is DIRECTLY proportional to the applied unbalanced force, and takes place in the DIRECTION of the force.
- Mathematical Form: F = dp/dt = d(mv)/dt = ma (when mass is constant)
- SI Unit of Force: newton (N) = kg·m/s²
Linear Momentum
- p = mv (vector, in direction of velocity)
- SI unit: kg·m/s
Important Implications
- Force is the CAUSE of acceleration, NOT velocity
- A ZERO net force means ZERO acceleration (but NOT necessarily zero velocity)
- Greater mass → less acceleration for the same force
Worked Problem
Q: A 5 kg block is pulled by a horizontal force of 20 N. If friction is 8 N, find acceleration. A: F_net = 20 — 8 = 12 N. a = F_net/m = 12/5 = 2.4 m/s².
4. Newton's Third Law of Motion
- Statement: Every action has an EQUAL and OPPOSITE reaction.
- Key Point: Action-reaction pairs act on DIFFERENT bodies, so they DON'T cancel each other
- Examples:
- Walking: foot pushes Earth backward, Earth pushes foot forward
- Rocket: exhaust gases pushed backward, gases push rocket forward
- Recoil of a gun: bullet forward, gun backward
Important Distinction
| Pairs | Act on | Effect |
|---|---|---|
| Action-Reaction (3rd Law) | Different bodies | DO NOT cancel |
| Balanced forces | Same body | CANCEL out (net force = 0) |
5. Impulse
- Impulse (J) = Force × Time = Change in momentum
- J = F·Δt = Δp = mv — mu
- Used when force acts for a VERY SHORT time (collisions, hitting a ball)
- Impulse is a VECTOR; SI unit: N·s or kg·m/s
Applications
- Catching a cricket ball: pull hands backward → increase Δt → reduce force
- Airbags in cars: increase collision time → reduce peak force
- Egg on concrete vs. foam: foam increases Δt, reduces F
6. Friction
Types
| Type | Description |
|---|---|
| Static Friction (f_s) | Prevents motion; adjusts up to a maximum value |
| Kinetic (Sliding) Friction (f_k) | Opposes motion once it starts |
| Rolling Friction | Much smaller than sliding friction |
Laws of Friction
- f_s ≤ μ_sN (static friction adjusts up to maximum)
- f_k = μ_kN (kinetic friction is constant for given surfaces)
- μ_s > μ_k (static > kinetic)
- Friction is INDEPENDENT of area of contact
Angle of Repose (θ)
- tanθ = μ_s
- At this angle, the block JUST begins to slide down the incline
Worked Problem
Q: A 10 kg block is on a horizontal surface with μ_s = 0.4 and μ_k = 0.3. Find force needed to start motion and to maintain uniform motion. A: N = mg = 100 N. f_s(max) = μ_sN = 0.4×100 = 40 N. f_k = μ_kN = 0.3×100 = 30 N. Force needed to start = 40 N. Force to maintain uniform motion = 30 N.
7. Circular Motion Dynamics
- For an object in uniform circular motion:
- Centripetal Force F_c = mv²/r (directed TOWARD centre)
- This force is PROVIDED by: tension (pendulum), gravity (satellite), friction (car turning)
- Banking of Roads: The outer edge of a curved road is raised to provide centripetal force through normal reaction. Ideal banking angle θ: tanθ = v²/rg
Worked Problem
Q: A car of mass 1200 kg takes a turn of radius 20 m at 15 m/s. Find frictional force needed. A: F_c = mv²/r = 1200×225/20 = 13500 N. Friction must provide this centripetal force.
8. Common Mistakes
- Action-reaction pairs DON'T cancel: They act on DIFFERENT objects
- Confusing mass and weight: Mass is constant; weight = mg varies with g
- Applying F = ma without finding net force: First RESOLVE all forces, find net, then apply
- Static friction is NOT always μ_sN: It is ≤ μ_sN; the ACTUAL value adjusts to the applied force
- Centripetal force is NOT a separate force: It is the NET force directed toward the centre
9. CBSE Exam Focus
- Statement and proof of all three laws (1+3+5 marks)
- Impulse-momentum theorem derivation and problems
- Friction numericals — inclined plane, horizontal surface
- Banking of roads derivation (5-mark)
- Motion of bodies connected by strings (Atwood machine)
10. Key Formulas
- F = ma = dp/dt
- p = mv
- J = F·Δt = Δp
- f_s ≤ μ_sN, f_k = μ_kN
- F_c = mv²/r = mω²r
- Banking: tanθ = v²/rg
11. Self-Test (5+ Q&A)
Q1: State Newton's second law in terms of momentum. A: F = dp/dt = d(mv)/dt. For constant mass, F = m(dv/dt) = ma.
Q2: A 0.5 kg ball at 20 m/s is caught. If caught in 0.02 s, find force. A: Impulse = Δp = 0 — (0.5×20) = -10 kg·m/s. F = |Δp|/Δt = 10/0.02 = 500 N.
Q3: A block slides down a 30° incline with μ_k = 0.2. Find acceleration. A: a = g(sinθ — μ_kcosθ) = 10(½ — 0.2×√3/2) = 10(0.5 — 0.173) = 3.27 m/s².
Q4: Why is it harder to start a heavy box moving than to keep it moving? A: μ_s > μ_k. The maximum static friction (needed to START motion) exceeds kinetic friction (opposing motion).
Q5: A cyclist leans while turning. Why? A: To provide centripetal force through the horizontal component of normal reaction. The angle of lean θ satisfies tanθ = v²/rg.
12. Conclusion
Newton's laws are the FOUNDATION of classical mechanics. The first law defines INERTIA, the second law QUANTIFIES force, and the third law reveals the INTERCONNECTEDNESS of forces. Friction is a practical force you encounter everywhere — learn its nuances well. Circular motion dynamics prepare you for gravitation and rotational mechanics in later chapters.
