Laws of Motion

Okay, so till now we learned how to DESCRIBE motion - distance, velocity, acceleration, projectile. But we never asked WHY does it move? Why does a ball stop? Why do you need to push a scooter to start it? That's what this chapter answers. This is the heart of Class 11.

Aristotle 2000 years ago said - to keep something moving, you need to keep pushing. If you stop pushing, it stops. Sounds logical, right? Because in daily life cycle chalane ke liye pedal marna padta hai, push karna band toh cycle ruk jaati hai.

But Galileo said - no, that's because of friction. If there was zero friction, a moving object would keep moving forever without push. Newton took this and made 3 laws. That's what we study.

Imagine you are sitting in Noida Metro, metro suddenly starts. You feel jerk backward. Why? Your lower body moves with metro, but upper body wants to stay at rest. That's Inertia of Rest - object wants to stay at rest if it is at rest.

Now metro is moving and suddenly brake at Botanical Garden. You lurch forward. Your body was moving, wants to keep moving, metro stopped, you didn't. That's Inertia of Motion.

Third - car takes sharp turn at Sector 18. You feel pushed outward to one side. Your body wants to go straight, car turns, so you feel outward. That's Inertia of Direction.

So inertia is like laziness. Rest wala wants to stay at rest, moving wala wants to keep moving same direction. The more mass, more inertia. That's why heavy truck is hard to push vs cycle. Mass = measure of inertia. Your mom's heavy almirah has huge inertia, you can't move alone.

Daily examples you see: Dust from carpet when you beat with stick - carpet moves, dust stays due to inertia of rest and falls. Blanket pull - dishes stay due to inertia if you pull fast. Coin on card trick - card flicked, coin falls in glass due to inertia of rest.

First law says: If net external force is zero, object at rest stays at rest, object in motion continues moving with same velocity (same speed same direction). Means if no force, no acceleration. Force is needed to change, not to maintain.

So why does cycle stop when you stop pedalling? Because friction and air resistance are external forces acting, not zero. If road was super smooth like ice and no air, cycle would go forever.

We define force here: anything that changes state of rest/motion or shape. Push, pull, friction, gravity all forces.

And we define inertial frame: frame where first law holds. Bus accelerating is non-inertial, you feel pseudo force backward. Ground is approximately inertial for us.

This is the most important law in physics. Almost whole physics runs on this.

First, what is momentum p = m × v? It's like how much 'dham' object has. Heavy truck 1000kg at 10m/s has huge momentum 10000, cycle 10kg at 10m/s only 100. To stop truck you need more effort. So momentum = mass × velocity. Vector quantity, direction same as velocity.

Second law: Rate of change of momentum is proportional to force. If you push harder, momentum changes faster. Mathematically F = dp/dt. If mass constant, then F = m × a. That's famous F=ma.

What does it mean in daily life? Two carts - empty and loaded with bricks. Same push - empty goes faster acceleration more because a=F/m. So for same force, acceleration inverse to mass.

Also, force not just ma, it's how fast momentum changes. This explains why we pull hands back while catching cricket ball. Ball has momentum. If you catch stiff, time very small, dp/dt large, force large on hands hurts. If you pull back, increase time t, reduce force. Same for karate chop - short time huge force breaks brick. Hammering nail - same.

Impulse J = F × Δt = change in momentum. Area under F-t graph = impulse. That's why you get more hurt if same force for longer time. Also why you jump from small height with bent knees - increase time reduce force.

Unit: Newton N = kg m/s². 1 N = force to give 1kg mass 1m/s² acceleration.

Third law says: To every action there is equal and opposite reaction, acting on different bodies.

Key point: Different bodies - they don't cancel! Because they act on different objects. If they acted on same body, nothing would move.

Walking: You push ground backward (action). Ground pushes you forward (reaction). You move forward because reaction acts on YOU, action acts on ground. Ground moves a bit back but Earth is huge mass, so negligible.

Swimming: You push water backward, water pushes you forward.

Horse-cart puzzle: Horse pulls cart forward, cart pulls horse backward equal. Then how does system move? Because horse also pushes ground backward, ground pushes horse forward bigger than cart pull. So system moves.

Book on table: Book weight down on table (action). Table pushes book up normal force (reaction). Both equal. Book at rest because weight mg and normal N are not action-reaction pair - they act on same body (book). Action-reaction pairs are always two bodies: book on table and table on book.

Rocket: Rocket pushes gas down (action), gas pushes rocket up (reaction). That's why rocket flies even in space - it carries its own mass to push.

Two friends on skates pushing each other: Friend A pushes B left, B pushes A right. Both move opposite, equal force but if masses different, acceleration different.

If no external force, total momentum of system stays constant. Like you and friend on frictionless ice. You push friend, you both move opposite such that m1v1 + m2v2 = 0 before push total 0. After push also 0. Momentum conserved.

Gun recoil: Before firing total momentum 0. Bullet mass m small velocity v large forward, gun mass M large velocity V small backward such that m v = M V opposite. That's why gun kicks back. Heavier gun kicks less.

Collision: Two balls collide. If no external force like friction, m1u1 + m2u2 = m1v1 + m2v2 after collision. This is used in car crash analysis, billiards.

Rocket: As fuel burns and throws gas down, mass decreases, velocity increases to conserve momentum.

Pulley system: Two masses m1, m2 hanging. Tension T same throughout string (ideal). Net force = (m1-m2)g, total mass = m1+m2, so acceleration a = (m1-m2)g/(m1+m2). Heavier goes down. If m1=m2, a=0 equilibrium.

Lift apparent weight: In lift accelerating up, you feel heavier N = m(g+a). Accelerating down, lighter N=m(g-a). Free fall a=g, N=0 weightlessness.

Real life always has friction. Without friction you can't walk, can't write with pen, car can't brake.

First draw Free Body Diagram: Isolate block, show all forces on it - weight mg down, normal N up perpendicular to surface, applied force F, friction f opposite motion, tension T along string. Then ΣF = ma separately for x and y.

Types of friction:
Static friction fs ≤ μ_s N - prevents motion, self-adjusts up to max. That's why heavy box doesn't move until you push hard enough. μ_s is static coefficient.
Kinetic friction fk = μ_k N - when sliding, constant, usually smaller than static max. So μ_s > μ_k. Means harder to start moving than to keep moving. You feel this pushing almirah - first push hardest, then easier.
Rolling friction much smaller - that's why wheels invented.

Graph: As you increase applied force, static friction increases equally till max μ_s N, then drops to kinetic μ_k N constant.

Angle of friction φ = arctan(μ_s). If incline angle less than φ, block doesn't slide.

Equilibrium: ΣF=0 and Σ torque =0 => no acceleration, rest or uniform velocity. Like book on table mg=N balanced.

Banking of road: At turn, need centripetal force v²/r. If road flat, only friction provides, can slip. If banked at angle θ, component of normal N sinθ provides centripetal. Ideal banking (no friction needed) tanθ = v²/rg. That's why highway curves are banked, cycle track banked. Also why you lean inward while turning cycle - to get component of normal.

Centripetal force is not new force - it's any force acting towards centre - tension, friction, normal component, gravity can provide.