50 physics questions, answered simply

Distance is the total length of the path travelled; it has only size (a scalar). Displacement is the shortest straight-line distance from the starting point to the final point, in a stated direction (a vector). If you walk once around a 400 m track and stop where you started, distance = 400 m but displacement = 0.

Speed tells how fast an object moves: speed = distance ÷ time. Velocity is speed in a given direction: velocity = displacement ÷ time. A car going round a circular road at a steady 40 km/h has constant speed, but its velocity keeps changing because its direction changes.

Acceleration is the rate of change of velocity: a = (v − u) ÷ t, where u is initial velocity and v is final velocity. Its SI unit is metre per second squared (m/s²). When velocity decreases, the acceleration is negative and is called retardation or deceleration.

For an object moving with uniform acceleration a in a straight line: (1) v = u + at, (2) s = ut + ½at², (3) v² = u² + 2as. Here u = initial velocity, v = final velocity, t = time and s = displacement.

Yes. Even if its speed stays the same, its direction changes at every point, so its velocity changes. A change in velocity means acceleration. This is why the Moon going round the Earth, or a stone whirled on a string, is accelerated motion.

An object stays at rest, or keeps moving in a straight line at constant speed, unless an unbalanced external force acts on it. This tendency of objects to resist a change in their state of motion is called inertia, so the first law is also called the law of inertia.

Inertia is the natural tendency of an object to resist any change in its state of rest or motion. Mass is the measure of inertia: the greater the mass, the greater the inertia. That is why it is harder to push a loaded truck than an empty cart.

Momentum is the product of an object's mass and velocity: p = m × v. Its SI unit is kg m/s. It is a vector and acts in the direction of velocity. A slow, heavy truck and a fast, light bullet can both have large momentum.

The rate of change of momentum of an object is proportional to the applied unbalanced force and takes place in the direction of the force. For constant mass this gives F = m × a. One newton (1 N) is the force that gives a 1 kg mass an acceleration of 1 m/s².

To every action there is an equal and opposite reaction. The two forces act on two different objects, so they do not cancel each other. When you push a wall, the wall pushes back on you with an equal force; when you walk, your foot pushes the ground backward and the ground pushes you forward.

Before firing, the total momentum of gun and bullet is zero. By the law of conservation of momentum, it must stay zero after firing. The bullet gains forward momentum, so the gun gains an equal momentum backward. The gun is much heavier, so it moves back with a much smaller velocity.

This is due to inertia of motion. When the bus stops, the lower part of the body in contact with the seat and floor stops with it, but the upper part tends to keep moving forward. When a bus starts suddenly, passengers fall backward for the same reason (inertia of rest).

The ball's momentum must be reduced to zero. Force = change in momentum ÷ time. By moving the hands back, the fielder increases the time taken to stop the ball, which reduces the force on his hands and the chance of injury. Sand pits for high jumpers work on the same idea.

Every object in the universe attracts every other object with a force that is directly 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, 6.67 × 10⁻¹¹ N m²/kg².

It is the acceleration produced in a freely falling object by the Earth's gravitational pull. Near the Earth's surface, g ≈ 9.8 m/s². In free fall, ignoring air resistance, a heavy stone and a light stone dropped together reach the ground at the same time, because g does not depend on the mass of the falling object.

Mass is the amount of matter in an object; it is measured in kg and stays the same everywhere. Weight is the force with which a planet pulls the object: W = m × g, measured in newtons. The Moon's gravity is about one-sixth of the Earth's, so an object weighs about one-sixth as much there, though its mass is unchanged.

Pressure = thrust (force) ÷ area. A sharp edge has a very small area, so the same force produces a much larger pressure, which cuts easily. For the opposite reason, school bags have broad straps and buildings have wide foundations: a larger area means less pressure.

Archimedes' principle says that an object immersed in a fluid feels an upward force (buoyant force) equal to the weight of fluid it displaces. A ship is shaped to displace a large volume of water whose weight equals the ship's weight, so it floats. A solid nail displaces only a little water, less than its own weight, so it sinks.

Work is done when a force moves an object in the direction of the force: W = F × s, measured in joules (J). If there is no displacement, no work is done, so a person holding a heavy box still does no work on it. If force and displacement are at right angles, as when the Earth's gravity acts on a satellite in circular orbit, the work done is also zero.

Kinetic energy is the energy an object has because of its motion: KE = ½ m v². Because speed is squared, doubling the speed makes the kinetic energy four times larger. This is why a car crash at high speed is far more dangerous.

Gravitational potential energy is the energy an object has because of its height above the ground: PE = m × g × h. Water stored high in a dam and a stretched rubber band (elastic potential energy) both store potential energy that can be turned into motion.

Energy can neither be created nor destroyed; it can only change from one form to another, and the total energy stays the same. When a ball falls, its potential energy decreases while its kinetic energy increases by the same amount (ignoring air resistance).

Power is the rate of doing work: P = W ÷ t. Its SI unit is the watt (W); 1 W = 1 J/s. The commercial unit of energy is the kilowatt-hour (kWh): 1 kWh = 3.6 × 10⁶ J. The '1 unit' on your electricity bill is 1 kWh, for example a 100 W bulb used for 10 hours.

Sound is a mechanical wave: it travels by making the particles of a medium (solid, liquid or gas) vibrate. In air it travels as a longitudinal wave of compressions and rarefactions. A vacuum has no particles to vibrate, so sound cannot pass through it. That is why astronauts on the Moon use radios to talk.

Sound travels fastest in solids, slower in liquids and slowest in gases. In air it travels at roughly 340 to 346 m/s at ordinary temperatures, in water about 1,500 m/s and in steel about 5,000 m/s or more. Speed in air also increases with temperature.

An echo is the sound heard again after it reflects from a large surface such as a cliff or wall. The sensation of a sound stays in our brain for about 0.1 second, so the reflected sound must arrive at least 0.1 s later to be heard separately. At about 344 m/s, this needs the reflecting surface to be at least about 17.2 m away.

Pitch depends on frequency, the number of vibrations per second, measured in hertz (Hz). Higher frequency gives a higher pitch, like a whistle. Loudness depends on amplitude, the size of the vibration: a larger amplitude gives a louder sound. Loudness is measured in decibels (dB).

Humans can hear frequencies from about 20 Hz to 20,000 Hz. Sound below 20 Hz is infrasound; above 20,000 Hz is ultrasound. Ultrasound is used in medical scanning of internal organs, finding cracks in metal blocks, cleaning delicate parts, and SONAR to measure the depth of the sea.

(1) The angle of incidence is equal to the angle of reflection. (2) The incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane. These laws apply to all reflecting surfaces, plane or curved.

The image is virtual (it cannot be taken on a screen), erect, the same size as the object, and as far behind the mirror as the object is in front of it. It is also laterally inverted: your right hand appears as the left hand of your image. That is why 'AMBULANCE' is written in reverse on vehicles.

A concave mirror curves inward and converges light; a convex mirror bulges outward and diverges light. Concave mirrors are used in torches and vehicle headlights, as shaving and make-up mirrors, by dentists, and in solar furnaces. Convex mirrors are used as rear-view mirrors in vehicles and as safety mirrors at sharp turns and in shops.

1/v + 1/u = 1/f, where u is the object distance, v is the image distance and f is the focal length, all measured from the pole of the mirror using the New Cartesian sign convention. The focal length is half the radius of curvature: f = R/2. Magnification m = h′/h = −v/u.

A convex mirror always forms an erect, diminished image, whatever the distance of the object. Because the image is smaller, the mirror shows a much wider area of the road behind, so the driver sees more traffic in a small mirror.

Refraction is the bending of light when it passes from one transparent medium to another, for example from air into water. It happens because light travels at different speeds in different media. Going into a denser medium, where it slows down, light bends towards the normal; coming out into a rarer medium, it bends away from the normal.

The absolute refractive index of a medium is n = c ÷ v, where c is the speed of light in vacuum (3 × 10⁸ m/s) and v is its speed in the medium. Water has n ≈ 1.33, ordinary glass about 1.5 and diamond about 2.42. A higher refractive index means light travels more slowly in that medium. Snell's law: sin i ÷ sin r = constant.

Light from the bottom of the pool bends away from the normal as it leaves water and enters air. Our eyes trace the rays back in straight lines, so the bottom appears raised. In the same way, the part of a pencil under water seems raised, making the pencil look bent at the surface.

A convex lens is thicker at the middle and converges light; a concave lens is thinner at the middle and diverges light. The lens formula is 1/v − 1/u = 1/f, using the New Cartesian sign convention measured from the optical centre. Magnification m = h′/h = v/u.

Power P = 1 ÷ f, with f in metres. Its unit is the dioptre (D). A convex lens has positive power and a concave lens negative power. A lens of focal length +0.5 m has power +2 D; an optician's prescription of −2.0 D means a concave lens of focal length 0.5 m.

When the object is beyond the focus (F), a convex lens forms a real, inverted image on the other side that can be caught on a screen, as in a camera or projector. When the object is between the focus and the lens, it forms a virtual, erect and magnified image on the same side, which is how a magnifying glass works. A concave lens always forms a virtual, erect, diminished image.

In myopia (short-sightedness), a person sees near objects clearly but not distant ones; the image forms in front of the retina. It is corrected with a concave lens. In hypermetropia (long-sightedness), distant objects are clear but near ones are blurred; the image forms behind the retina. It is corrected with a convex lens.

Each colour in white light bends by a different amount in glass: violet bends the most and red the least. This splitting is called dispersion and gives the band of colours VIBGYOR: violet, indigo, blue, green, yellow, orange and red. A rainbow forms in the same way when sunlight is dispersed and reflected by tiny raindrops.

Tiny particles in the air scatter light of shorter wavelengths, such as blue, much more than longer wavelengths like red. This scattered blue light reaches us from all directions, so the sky looks blue. At sunrise and sunset, sunlight travels a much longer path through the atmosphere; most blue light is scattered away, and mainly red and orange light reaches our eyes.

Starlight passes through layers of air whose density and temperature keep changing, so it is refracted by varying amounts (atmospheric refraction). Stars are so far away that they act like point sources, and their light flickers. Planets are much nearer and look like small discs; the flickering from different points evens out, so they do not twinkle.

Electric current is the rate of flow of electric charge: I = Q ÷ t. Its SI unit is the ampere (A); 1 A = 1 coulomb per second. It is measured with an ammeter connected in series. By convention, current flows from the positive to the negative terminal, opposite to the flow of electrons.

At constant temperature, the current through a conductor is directly proportional to the potential difference across its ends: V = I × R, where R is the resistance in ohms (Ω). Potential difference is measured with a voltmeter connected in parallel.

R = ρ × l ÷ A. Resistance increases with the length (l) of the wire, decreases as its cross-sectional area (A) increases, and depends on the material through its resistivity (ρ). For metals, resistance also rises with temperature. Copper and aluminium have low resistivity and are used for wiring; nichrome has high resistivity and is used in heaters.

In series, resistances add up (R = R₁ + R₂ + …) and the same current flows through each, so if one bulb fuses all go off. In parallel, 1/R = 1/R₁ + 1/R₂ + …; each appliance gets the full mains voltage and can be switched on or off independently. That is why household wiring uses parallel connections.

When current flows through a resistor, heat is produced: H = I² R t (Joule's law of heating). Electric irons, heaters and kettles use this effect. A fuse is a thin wire of low melting point connected in series; if the current becomes too high, the fuse wire melts and breaks the circuit, protecting the appliances and wiring.

P = V × I = I² R = V² ÷ R, measured in watts. For example, an appliance working at 220 V and drawing 5 A uses 220 × 5 = 1,100 W, or 1.1 kW. Running it for 2 hours uses 1.1 × 2 = 2.2 kWh, which is 2.2 units of electricity.

Right-hand thumb rule: hold a current-carrying straight wire in your right hand with the thumb pointing along the current; your curled fingers show the direction of the magnetic field lines around it. Fleming's left-hand rule: stretch the thumb, forefinger and middle finger of the left hand at right angles; if the forefinger points along the magnetic field and the middle finger along the current, the thumb gives the direction of force on the conductor.