Physics Basics Notes: Motion, Force

Physics explains how things move, why they move and how we see the world around us. General science is part of almost every competitive examination, including SSC, railways, banking, defence, state-level exams and the UPSC Prelims, and physics questions are usually simple, based on concepts, units and everyday examples. This note covers the basics of motion, force, gravitation, work and energy, pressure, and light, with formulas, units, solved examples and tips for students, in simple language.

Motion

Motion is the change in the position of an object with time. Distance is the total length of the path travelled and is a scalar (it has only magnitude). Displacement is the shortest distance between the starting and ending points in a given direction and is a vector (it has magnitude and direction). Speed is distance divided by time; velocity is displacement divided by time. Acceleration is the rate of change of velocity: a = (v − u)/t, measured in m/s². A negative acceleration is called retardation or deceleration. When an object moves in a circle at constant speed, its direction keeps changing, so its velocity is changing, and it has acceleration towards the centre.

The three equations of uniformly accelerated motion are: v = u + at, s = ut + ½at² and v² = u² + 2as, where u is the initial velocity, v is the final velocity, a is acceleration, t is time and s is displacement. Example: a car starts from rest and accelerates at 2 m/s² for 5 seconds. Its final speed is v = 0 + 2 × 5 = 10 m/s, and the distance travelled is s = ½ × 2 × 5² = 25 m. A body thrown upwards has deceleration g (9.8 m/s²) and reaches the maximum height when its velocity becomes zero.

Force and Newton's Laws of Motion

Inertia is the tendency of a body to resist a change in its state, and it depends on mass. Momentum is the product of mass and velocity (p = mv), with the unit kg m/s. The law of conservation of momentum says that the total momentum of an isolated system remains constant. The SI unit of force is the newton (N), where 1 N = 1 kg m/s². Friction is the force that opposes motion between surfaces in contact; it can be useful (walking, brakes) or harmful (wear and heat).

Gravitation

Newton's universal law of gravitation states that every object attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G m₁m₂/r². G is the universal gravitational constant. The acceleration due to gravity on Earth, g, is about 9.8 m/s², and it is the same for all bodies in the absence of air resistance, whatever their mass. It is greater at the poles than at the equator, and decreases as we go up or deep inside the Earth. Mass is the amount of matter in a body and does not change (unit: kilogram), while weight is the force of gravity on the body (W = mg, unit: newton) and changes from place to place. On the Moon, the weight of an object is about one-sixth of its weight on Earth because g is smaller there. The escape velocity from the Earth is about 11.2 km/s, and the orbital velocity near the surface is about 7.9 km/s.

Work, Energy and Power

Work is done when a force moves an object: W = F × d × cos θ, with the unit joule (J). If the displacement is zero, or the force is perpendicular to the motion, the work done is zero. Energy is the capacity to do work. Kinetic energy is the energy of motion (KE = ½mv²), and potential energy is the energy of position (PE = mgh). Energy cannot be created or destroyed, only changed from one form to another: this is the law of conservation of energy. Power is the rate of doing work (P = W/t), with the unit watt (W), where 1 W = 1 J/s. One kilowatt-hour (kWh), the unit of electricity billing, equals 3.6 million joules, and 1 horsepower is about 746 W.

Pressure and Fluids

Pressure is force per unit area: P = F/A, with the unit pascal (Pa). A sharp knife cuts better because the small area gives high pressure. Pascal's law says that pressure applied to a fluid in a closed container is transmitted equally in all directions, which is the principle of the hydraulic lift and brakes. Archimedes' principle says that a body immersed in a fluid experiences an upward force (buoyancy) equal to the weight of the fluid it displaces. An object floats if its density is less than that of the fluid. This is why a ship floats, and why it is easier to float in sea water than in river water. Density is mass per unit volume; the density of water is 1,000 kg/m³ (1 g/cm³).

Light: Reflection

Light travels in straight lines at a speed of about 3 × 10⁸ m/s in vacuum. The laws of reflection say that the angle of incidence equals the angle of reflection, and the incident ray, the reflected ray and the normal lie in the same plane. A plane mirror forms a virtual, erect image of the same size, as far behind the mirror as the object is in front. A concave mirror converges light and is used in shaving mirrors, torches, headlights and by dentists. A convex mirror diverges light, gives a wider field of view and is used as a rear-view mirror in vehicles. The mirror formula is 1/v + 1/u = 1/f, where u is the object distance, v is the image distance and f is the focal length; the focal length is half of the radius of curvature. Example: for a concave mirror of focal length 20 cm and an object 30 cm away (u = −30, f = −20 in the sign convention), 1/v = 1/f − 1/u = −1/20 + 1/30 = −1/60, so v = −60 cm; the image is real and 60 cm in front of the mirror.

Light: Refraction and Lenses

Refraction is the bending of light when it passes from one medium to another because its speed changes. Snell's law states that sin i / sin r is constant, and this constant is the refractive index n = c/v, the ratio of the speed of light in vacuum to that in the medium. The refractive index of glass is about 1.5, so light in glass travels at 3 × 10⁸/1.5 = 2 × 10⁸ m/s. Total internal reflection occurs when light moves from a denser to a rarer medium at an angle greater than the critical angle; it explains the sparkle of diamonds, mirages and the working of optical fibres. A convex lens converges light and is used in magnifying glasses, cameras and spectacles for hypermetropia; a concave lens diverges light and is used for myopia. The lens formula is 1/v − 1/u = 1/f, and the power of a lens is P = 1/f (f in metres), measured in dioptres (D). A lens of power 2 D has a focal length of 0.5 m. The power is positive for a convex lens and negative for a concave lens.

Light: Human Eye, Dispersion and Scattering

The human eye forms a real, inverted image on the retina, which the brain interprets as upright. The cornea and lens focus light, the iris controls the size of the pupil, and the lens changes its focal length by the ciliary muscles (accommodation). Myopia (short-sightedness) means that distant objects look blurred and is corrected by a concave lens; hypermetropia (long-sightedness) means that near objects look blurred and is corrected by a convex lens; presbyopia occurs in old age; astigmatism is corrected by a cylindrical lens. Dispersion is the splitting of white light into its seven colours by a prism: violet, indigo, blue, green, yellow, orange and red (VIBGYOR); red bends the least and violet bends the most. A rainbow is formed by the dispersion and total internal reflection of sunlight in raindrops. Scattering explains why the sky is blue (blue light is scattered more than red by air molecules) and why the Sun looks red at sunrise and sunset (the blue light is scattered away over a long path).

Quick Revision

• v = u + at; s = ut + ½at²; v² = u² + 2as; F = ma; p = mv; W = Fd; P = W/t.
• g = 9.8 m/s²; escape velocity from Earth = 11.2 km/s; weight on the Moon is one-sixth.
• Concave mirror converges; convex mirror diverges; myopia needs a concave lens; hypermetropia needs a convex lens.
• Power of lens = 1/f (in metres) in dioptres; refractive index n = c/v.

Physics is best learned with examples from daily life. Revise the formulas and units on one page, solve a few numerical problems each day, and connect each law with an event you see around you.

Related Notes to Read Next

Continue your preparation with these related notes from the same subject:

• Chemistry Basics Notes for Competitive Exams
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• All General Science notes

Frequently Asked Questions (FAQ)

What is the difference between distance and displacement?

Distance is the total path length travelled and is a scalar, while displacement is the shortest straight-line distance between the start and end points with direction, and it is a vector.

What is Newton’s first law of motion?

Newton’s first law states that a body remains at rest or in uniform motion in a straight line unless an external force acts on it. It is also called the law of inertia.

What is the formula of Newton’s second law?

Newton’s second law is F = ma, where F is the force, m is the mass and a is the acceleration.

What is the difference between mass and weight?

Mass is the amount of matter in a body and does not change, while weight is the force of gravity acting on the body, which changes from place to place.

What is the value of g on Earth?

The acceleration due to gravity on Earth is about 9.8 m/s².

What is escape velocity?

Escape velocity is the minimum speed needed to escape the gravitational pull of a planet. For the Earth it is about 11.2 km/s.

What is the SI unit of power?

The SI unit of power is the watt, which is one joule per second.

What does Archimedes’ principle state?

It states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.

Which mirror is used as a rear-view mirror in vehicles?

A convex mirror is used because it gives a wider field of view and forms an erect, diminished image.

What is the refractive index?

The refractive index of a medium is the ratio of the speed of light in vacuum to its speed in that medium.

Which lens corrects myopia?

A concave lens corrects myopia (short-sightedness), and a convex lens corrects hypermetropia (long-sightedness).

Why is the sky blue?

The sky looks blue because the molecules in the air scatter blue light more than red light, and this scattered blue light reaches our eyes from all directions.