The full, readable lecture — Newton's three laws, momentum & impulse, conservation of momentum, collisions, friction and the inclined plane. As you scroll, the panel on the right brings each idea to life with a real-life scene you already know: a braking bus, a loaded trolley, a recoiling gun, a fielder's catch.
1 — Force & Newton's first law (inertia)
- Force — an agent that changes, or tends to change, a body's state of rest or uniform motion. A vector; SI unit the newton (N), where 1 N = 1 kg·m/s².
- Inertia — the natural tendency of a body to resist any change in its state of rest or uniform motion. Mass is the measure of inertia.
Newton's first law: a body remains at rest, or continues to move with uniform velocity in a straight line, unless an unbalanced external force acts on it. It is also called the law of inertia.
Karachi moment: when the bus on University Road brakes hard, you lurch forward — your body was moving and keeps moving by inertia, as the panel shows. The seat-belt supplies the backward force that stops you. When the bus pulls away suddenly you jerk backward, for the very same reason.
2 — Newton's second law (F = ma)
Newton's second law: when an unbalanced force acts on a body, it produces an acceleration in the direction of the force; the acceleration is directly proportional to the force and inversely proportional to the mass.
The equation of dynamicsF = m a · a = F / m
1 N = 1 kg × 1 m/s² · weight W = m g (g ≈ 9.8 m/s²)
On the right, drag the two sliders: push a shopping cart at the supermarket harder and it speeds up faster; pile on groceries (more mass) and the same push barely moves it. The number a = F/m updates live in SI units. It is why an empty Suzuki pickup darts away from the signal, but loaded with mango crates it crawls.
worked numerical · f = ma
A 200 N force acts on a 250 kg rickshaw starting from rest. Find the acceleration, and the velocity after 5 s.
a = F/m = 200/250 = 0.8 m/s² · v = u + at = 0.8 × 5 = 4 m/s
3 — Newton's third law (action & reaction)
Newton's third law: to every action there is an equal and opposite reaction. Forces always occur in pairs, acting on two different bodies — so they never cancel each other.
- Walking — your foot pushes the road backwards; the road pushes you forwards.
- Gun & bullet — the gun pushes the bullet forwards; the bullet pushes the gun backwards (recoil), as the panel shows.
- Balloon & rocket — air (or hot gas) is pushed one way; the balloon or rocket is pushed the other. No air outside is needed.
Common error: action and reaction never balance because they act on different bodies. A book resting on a table is in first-law equilibrium (weight vs the table's normal force on the book) — that is not the third-law pair.
4 — Momentum & impulse
- Momentum (p) — the quantity of motion, p = m v. A vector along the velocity. SI unit kg·m/s (= N·s).
- Impulse (J) — a force acting for a time, J = F t. Impulse equals the change in momentum.
Second law, momentum formF = (mv − mu)/t ⇒ F t = mv − mu
impulse = change in momentum · units: N·s = kg·m/s
Why a fielder pulls his hands back: the ball's momentum change (mv − mu) is fixed, so F t is fixed. By drawing his hands back he increases t, so the force F on his palms decreases — the panel contrasts a hard stop with a soft one. The same physics is behind car crumple zones and bending your knees on landing.
worked numerical · the fielder's catch
A 0.15 kg cricket ball at 30 m/s is stopped in 0.05 s. Find the force. And if stopped in 0.5 s?
F = (0 − 0.15×30)/0.05 = 90 N on the palms · with t = 0.5 s → only 9 N
5 — Friction: static & kinetic
Friction is the force that opposes relative motion (or attempted motion) between two surfaces in contact. It arises from the interlocking of surface irregularities and molecular adhesion.
- Static friction — acts while the body is still at rest; it is self-adjusting up to a maximum called limiting friction.
- Kinetic friction — acts once sliding begins; slightly smaller than limiting static friction, and roughly constant.
Coefficient of frictionμ = F / R · f = μ m g (level ground) · μ_k < μ_s
Use the two buttons on the right to switch the surface: the same shove sends the box gliding across smooth ice but it grinds to a stop on rough sandpaper. This is why a skidding car (kinetic friction) stops in a longer distance than one whose tyres keep gripping — the idea behind ABS brakes.
worked numerical · friction
A 30 kg crate just starts to slide under 117.6 N. Find μ_s. (g = 9.8)
R = mg = 294 N ⇒ μ_s = 117.6/294 = 0.4
6 — Conservation of momentum & collisions
Law of conservation of momentum: when no external force acts on a system, the total momentum stays constant. For two bodies that collide:
Two-body collisionm₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
It follows from the second and third laws — the colliding bodies push on each other equally and oppositely for the same time, so their momentum changes cancel. On the right, a Newton's cradle shows it perfectly: lift one steel ball, release it, and a single ball leaps off the far end at the same speed.
| Property | Elastic | Inelastic |
|---|
| Momentum | conserved | conserved |
| Kinetic energy | conserved | lost (heat, sound, deformation) |
| Example | carrom / cradle | mud on a wall; coupled trolleys |
worked numerical · recoil
A 4 kg rifle fires a 20 g bullet at 400 m/s. Find the recoil velocity.
0 = (0.02 × 400) + 4V ⇒ V = −2 m/s (backwards)
7 — Motion on an inclined plane
On a slope of angle θ, resolve the weight mg into two rectangular components — exactly the vector skills from Unit 2:
Incline of angle θalong the slope (down): mg sin θ
perpendicular to slope: R = mg cos θ
frictionless: a = g sin θ · with friction: a = g(sin θ − μ cos θ)
The steeper the ramp, the larger sin θ and the faster the slide — exactly what a loader at Jodia Bazaar knows: a long, gentle plank lets the sacks slide down slowly under control; a steep one lets them crash. The panel resolves the crate's weight into its two components as θ grows.
worked numerical · incline
A 5 kg block slides down a frictionless 30° incline. Find a and the normal reaction. (g = 9.8)
a = g sin30° = 4.9 m/s² · R = mg cos30° = 42.4 N
8 — Exam recap
- 1st law: inertia — no unbalanced force, no change in velocity; mass measures inertia.
- 2nd law: F = ma; W = mg; 1 N = 1 kg·m/s².
- 3rd law: equal & opposite forces on two different bodies.
- Impulse F t = mv − mu; longer stopping time → gentler force.
- Conservation: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ when no external force acts.
- Elastic collisions conserve kinetic energy; inelastic do not (momentum conserved in both).
- Friction μ = F/R; μ_k < μ_s; on level ground R = mg.
- Incline: mg sin θ along, mg cos θ in; a = g(sin θ − μ cos θ).