Units, motion, Newton's laws and gravitation

Core facts

Seven SI base units:

Quantity	Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

Scalar has magnitude only (mass, speed, distance, energy). Vector has magnitude and direction (velocity, force, displacement, acceleration, momentum).
Speed = distance / time. Velocity = displacement / time. Acceleration = change in velocity / time; unit m/s².
Newton's laws:
1. First (inertia): a body stays at rest or in uniform motion in a straight line unless an external force acts.
2. Second: force = mass x acceleration (F = ma); the rate of change of momentum is the force.
3. Third: every action has an equal and opposite reaction (on different bodies).
Unit of force: newton (N) = kg m/s². Momentum = mass x velocity (kg m/s).
Mass is the amount of matter (kg, same everywhere). Weight is the force of gravity on the body (W = mg, in newton) and changes with place.
g = 9.8 m/s² on Earth's surface. On the Moon, g is about one-sixth of Earth's.
Escape velocity from Earth: 11.2 km/s. From the Moon: about 2.4 km/s.
Gravitational constant G = 6.67 x 10⁻¹¹ N m²/kg². Measured by Cavendish (1798).

Explained

Equations of motion (uniform acceleration, initial velocity u, final v, time t, distance s)

v = u + at
s = ut + ½at²
v² = u² + 2as

Everyday examples of the laws

First law: passengers lurch forward when a bus brakes; dust falls off a beaten carpet.
Second law: a heavier object needs a bigger force for the same acceleration; a cricketer draws back the hands while catching to lengthen the stopping time and reduce the force.
Third law: a gun recoils when fired; a rocket moves up as exhaust gases are pushed down; swimmers push water backwards.

Conservation of momentum. In an isolated system, total momentum before and after a collision is the same. This explains gun recoil and rocket propulsion.

Universal law of gravitation (Newton). Every two masses attract with a force proportional to the product of the masses and inversely proportional to the square of the distance: F = G m1 m2 / r².

Variation of g

g is greater at the poles than at the equator (Earth is slightly flattened and spinning).
g decreases with height above the surface and also with depth below it; it is zero at the centre of Earth.
All bodies fall with the same acceleration in a vacuum. On the Moon in 1971 an Apollo 15 astronaut showed a hammer and a feather landing together.

Kepler's laws of planetary motion

Planets move in elliptical orbits with the Sun at one focus.
A line joining planet and Sun sweeps equal areas in equal times (planets move faster near the Sun).
The square of the orbital period is proportional to the cube of the semi-major axis.

Circular motion. A body moving in a circle needs a centripetal force towards the centre. Gravity provides it for planets and satellites. Centrifugal force is an apparent (pseudo) force felt in the rotating frame; cream separators and washing-machine dryers use it.

Weightlessness. An astronaut in orbit is in continuous free fall with the spacecraft, so feels no weight although gravity still acts. Mass does not change.

Common traps

✗ "Mass of an astronaut is zero in orbit." ✓ Mass is unchanged; only the apparent weight is zero.
✗ "g is greatest at the equator." ✓ g is greatest at the poles, least at the equator.
✗ "Weight is measured in kilograms." ✓ Weight is a force, in newton; kg measures mass.
✗ "Action and reaction cancel because they are equal and opposite." ✓ They act on different bodies, so they do not cancel.
✗ "Escape velocity depends on the mass of the projectile." ✓ It depends on the planet's mass and radius only.
✗ "Velocity and speed are the same." ✓ Velocity is a vector; average velocity can be zero while speed is not.

Quick revision

Seven SI base units: m, kg, s, A, K, mol, cd.
F = ma; unit newton = kg m/s².
Newton's first law = inertia; third law = action-reaction on different bodies.
Momentum = mv; conserved in isolated systems.
g = 9.8 m/s²; Moon about one-sixth; highest at poles.
Escape velocity: Earth 11.2 km/s; Moon about 2.4 km/s.
G = 6.67 x 10⁻¹¹ N m²/kg²; measured by Cavendish.
Kepler: ellipse, equal areas, T² proportional to a³.
Weightlessness in orbit = free fall, not zero gravity.

Go deeper: Deeper, Mains writing (beyond what APPSC Paper I usually asks)

Deeper Advanced

Inertia of rest, motion and direction are the three forms the first law is taught in.
Impulse = force x time = change in momentum. Airbags and crumple zones lengthen the time of impact so the average force falls.
Orbital velocity near Earth's surface is about 7.9 km/s. Escape velocity is sqrt(2) times orbital velocity at the same radius. Escape velocity does not depend on the mass of the escaping body.
Geostationary orbit: period equal to Earth's rotation (about 24 hours), orbit above the equator at about 35,786 km. Low Earth orbit satellites circle in roughly 90 minutes.
Einstein's general relativity (1915) treats gravity as curvature of space-time. Gravitational waves were first detected by LIGO in September 2015 (announced February 2016); the 2017 Nobel Prize in Physics went to Weiss, Barish and Thorne. A LIGO observatory is planned in India at Hingoli, Maharashtra.
2019 SI redefinition (in force 20 May 2019): the kilogram is now defined by fixing the Planck constant, ending the platinum-iridium prototype. The ampere, kelvin and mole are likewise defined by fixed values of the elementary charge, the Boltzmann constant and the Avogadro constant.
Friction is a contact force opposing relative motion. Static friction is greater than kinetic (sliding) friction, which is greater than rolling friction; this is why wheels and ball bearings reduce wear.

Mains writing Mains writing

Frame: Newton's laws are the physical basis of launch vehicles and satellite orbits, so they underpin India's space programme and its applications.
Analysis:
- Third law: rocket thrust comes from expelling exhaust, so it works in vacuum.
- Escape velocity and orbital mechanics set the fuel needed; hence multi-stage rockets and gravity-assist trajectories.
- Geostationary and low Earth orbits serve different needs (communication versus imaging).
Way forward: build reusable launchers, cut the cost of lift to orbit and apply orbital mechanics to debris tracking.
Example: Chandrayaan-3 soft landing near the lunar south pole (August 2023) relied on precise control of velocity against the Moon's gravity (g about one-sixth of Earth's).

Medha AI writes its own notes and checks them against the sources listed. Medha AI is an independent preparation service. It is not affiliated with, endorsed by or connected to APPSC, TSPSC, MPSC, UPSC or any other commission or government body.

2.1.1 Units, motion, Newton's laws and gravitation

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