Motion & Forces
Master the laws of motion, types of forces—gravitational, frictional, centripetal, centrifugal—Newton's three laws, momentum, inertia, impulse, and conservation principles.
1. Types of Motion & Frame of Reference
Motion is a change in position of an object with respect to time and a reference point. Key types include:
| Type of Motion |
Description |
Example |
| Translational |
All parts move the same distance in same direction |
A car moving on a straight road |
| Rotational |
Body moves around a fixed axis |
Earth's rotation, spinning top |
| Oscillatory |
To-and-fro motion about a mean position |
Simple pendulum, vibrating string |
| Periodic |
Motion that repeats itself at regular intervals |
Motion of planets around the Sun |
| Uniform Circular |
Motion along a circular path with constant speed |
Satellite orbiting Earth |
Frame of Reference: A coordinate system relative to which motion is measured. Inertial frames are non-accelerating (Newton's laws hold directly); non-inertial frames require pseudo-forces.
2. Scalars & Vectors in Motion
Understanding the difference between scalars and vectors is foundational for motion:
| Quantity |
Type |
SI Unit |
Formula |
| Distance |
Scalar |
m |
Total path length traveled |
| Displacement |
Vector |
m |
Shortest path from initial to final position |
| Speed |
Scalar |
m/s |
Distance / Time |
| Velocity |
Vector |
m/s |
Displacement / Time |
| Acceleration |
Vector |
m/s² |
(v - u) / t |
| Momentum |
Vector |
kg·m/s |
p = m × v |
| Force |
Vector |
N (Newton) |
F = ma |
Equations of Motion (Constant Acceleration):
- v = u + at (Relation between velocities and time)
- s = ut + ½at² (Relation between displacement and time)
- v² = u² + 2as (Relation without time)
- sn = u + a(2n - 1)/2 (Distance traveled in nth second)
Where: u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement
3. Newton's Laws of Motion
Newton's three laws form the foundation of classical mechanics:
| Law |
Statement |
Key Concept |
Example |
| First Law |
An object at rest stays at rest; an object in motion stays in motion with constant velocity, unless acted upon by an unbalanced external force. |
Inertia — resistance to change in state of motion |
A book on a table remains at rest until pushed. |
| Second Law |
The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force. (F = ma) |
Quantifies force — 1 N = 1 kg·m/s² |
A tennis racket applies force to accelerate the ball. |
| Third Law |
Every action has an equal and opposite reaction. (Forces always occur in pairs.) |
Action-Reaction — forces on different bodies |
When you jump, you push the Earth down (action) and Earth pushes you up (reaction). |
Impulse: Impulse = Force × Time = Change in momentum. It is a vector quantity (SI unit: N·s or kg·m/s). Cricketer pulling his hands back while catching a ball increases the time of impact, reducing the force experienced.
4. Types of Forces
Forces are broadly classified into Contact Forces and Non-Contact Forces:
Contact Forces
| Force |
Description |
Key Fact for Exams |
| Friction |
Opposes relative motion between surfaces in contact |
F = μN (μ = coefficient of friction, N = normal reaction). Static > Kinetic > Rolling friction. |
| Normal Reaction |
Perpendicular force exerted by a surface on an object |
Always acts perpendicular to the surface of contact. |
| Tension |
Force transmitted through a string/rope when pulled |
Tension is the same throughout an ideal massless, inextensible string. |
| Spring Force |
Restoring force proportional to displacement (Hooke's Law) |
F = -kx (k = spring constant, x = displacement from natural length) |
Non-Contact Forces
| Force |
Description |
Key Fact for Exams |
| Gravitational Force |
Force of attraction between any two masses |
F = Gm₁m₂/r². g = 9.8 m/s² at Earth's surface. g decreases with altitude and depth. |
| Electromagnetic Force |
Force between charged particles (electric & magnetic) |
Much stronger than gravity (~10³⁶ times). Governs atomic and molecular interactions. |
| Nuclear Forces |
Strong and weak nuclear forces binding nucleus |
Strongest force in nature. Acts over extremely short range (~10⁻¹⁵ m). |
| Centripetal Force |
Force required to keep a body moving in a circular path |
Fc = mv²/r. Directed toward the center. Without it, the body would fly off tangentially. |
| Centrifugal Force |
Pseudo-force felt in a rotating reference frame |
Directed outward, away from the center. It is a fictitious force experienced in non-inertial frames. |
5. Friction, Gravity & Conservation Laws
Friction is a resistive force that opposes relative motion between surfaces in contact. It is of three types:
- Static Friction (fs): Opposes the initiation of motion. Maximum static friction fs(max) = μsN.
- Kinetic/Sliding Friction (fk): Opposes ongoing motion. fk = μkN. Usually μk < μs.
- Rolling Friction (fr): Opposes rolling motion. Much smaller than static and kinetic friction. This is why wheels were invented.
Methods to reduce friction: Lubrication (oil/grease), polishing surfaces, using ball bearings, streamlining shapes, and using wheels/rollers.
Gravity (Universal Gravitation):
- Every particle attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
- Acceleration due to gravity (g): At Earth's surface, g = GM/R² ≈ 9.8 m/s².
- Variation of g:
- With altitude: g' = g(1 - 2h/R) for h << R.
- With depth: g' = g(1 - d/R) inside Earth.
- Due to rotation of Earth: g is maximum at poles, minimum at the equator.
- Escape Velocity (ve): Minimum velocity required to escape Earth's gravitational pull. ve = √(2GM/R) = √(2gR) ≈ 11.2 km/s.
Conservation Laws:
- Conservation of Linear Momentum: In the absence of external forces, the total momentum of an isolated system remains constant. (Momentum before = Momentum after)
- Conservation of Energy: Energy can neither be created nor destroyed — it can only be converted from one form to another.
- Conservation of Angular Momentum: In the absence of external torque, the angular momentum of a system remains constant. (Used to explain why a spinning ice skater spins faster by pulling arms in.)
Historical Development of Classical Mechanics
- c. 330 BCE — Aristotelian Physics: Aristotle proposed that heavier objects fall faster, and that a force is required to maintain motion (a view later disproven by Galileo and Newton).
- c. 1590-1600 — Galileo's Experiments: Galileo Galilei conducted experiments with inclined planes and free-falling objects, establishing the concept of inertia and uniform acceleration.
- 1687 — Newton's Principia Mathematica: Sir Isaac Newton published 'Philosophiæ Naturalis Principia Mathematica', laying down the three laws of motion and the law of universal gravitation.
- 1905-1915 — Einstein's Theory of Relativity: Albert Einstein's special and general theories of relativity redefined concepts of motion, gravity, and space-time at high velocities and strong gravitational fields.
Key Questions & Answers
- What is Newton's first law of motion also known as?
- The **Law of Inertia** — a body at rest remains at rest, and a body in motion continues in uniform motion unless acted upon by an external unbalanced force.
- State Newton's Second Law of Motion mathematically.
- **F = ma** (Force = Mass × Acceleration). The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.
- What is the SI unit of momentum?
- **kg·m/s** (Kilogram meter per second). Momentum = mass × velocity.
- What is the difference between mass and weight?
- **Mass** is the amount of matter (scalar, constant everywhere, measured in kg). **Weight** is the gravitational force on an object (vector, W = mg, varies with gravity).
Memory Aids
- Mnemonic 1: Newton's Three Laws (Number Trick): Remember them by the number sequence: • **1st Law (Law of Inertia)**: Body at rest stays at rest; body in motion stays in motion — I for Inertia. • **2nd Law**: F = ma — F for Force formula. • **3rd Law**: Every action has an equal and opposite reaction — P for Pair of forces.
- Mnemonic 2: Types of Friction Order: Friction types from highest to lowest: • S — Static Friction (highest, required to start motion) • K — Kinetic/Sliding Friction (moderate, opposes motion) • R — Rolling Friction (lowest, wheels reduce it)
- Mnemonic 3: Factors Affecting Friction: Key factors: • N — Nature of surfaces in contact • R — Roughness of the surfaces • I — Independent of area of contact (trick: 'I' reminds you it's Independent of area)
Common Exam Traps
- Trap 1: Confusing mass with weight. Mass is constant regardless of location; weight changes with gravitational field strength (e.g., weight on the Moon is 1/6th that on Earth, but mass remains the same).
- Trap 2: Believing that a body in uniform circular motion has no acceleration. In uniform circular motion, the speed is constant, but the direction keeps changing — hence there is centripetal acceleration directed toward the center.
- Trap 3: Thinking that zero net force means the body must be at rest. According to Newton's first law, zero net force means the body is either at rest OR in uniform motion (constant velocity).
- Trap 4: Confusing momentum with kinetic energy. Momentum (p = mv) is a vector; kinetic energy (KE = ½mv²) is a scalar. A body can have kinetic energy but zero net momentum if two equal masses move in opposite directions.