General Science

Describing motion

• Rest and motion are relative: an object is in motion if its position changes with time compared with a reference point.
• Distance is the total length of the path travelled (scalar). Displacement is the shortest straight-line distance from the initial to the final position, with direction (vector). Distance ≥ |displacement|; they are equal for straight-line motion in one direction.
• Speed = distance / time (scalar). Velocity = displacement / time (vector).
• Average speed = total distance / total time. If an object covers equal distances at speeds $v_1$ and $v_2$, the average speed is $\frac{2v_1{v}_2}{v_1+v_2}$ (the harmonic mean), not the simple average.
• Acceleration = change in velocity / time; unit m/s². Retardation (deceleration) is negative acceleration.
• Uniform motion: equal distances in equal times (constant velocity). Non-uniform motion: velocity changes.

Equations of motion (constant acceleration)

where $u$ = initial velocity, $v$ = final velocity, $a$ = acceleration, $t$ = time, $s$ = displacement. The distance covered in the $n$-th second is $s_n=u+\frac{a}{2}(2n-1)$.

Graphs

• Distance–time graph: the slope gives speed. A straight line inclined upward = uniform speed; a horizontal line = at rest.
• Velocity–time graph: the slope gives acceleration; the area under the graph gives displacement. A horizontal line = uniform velocity; an inclined straight line = uniform acceleration.

Free fall

Near the Earth, all bodies fall with the same acceleration $g\approx 9.8{\text{m/s}}^2$ (in the absence of air resistance) — Galileo's result, shown by the feather-and-coin experiment in a vacuum (Newton's tube). For a body dropped from rest: $v=gt$, $h=\frac{1}{2}g{t}^2$. For a body thrown upward with speed $u$: maximum height $H=\frac{u^2}{2g}$; time of ascent $=u/g$; total time of flight $=2u/g$.

Circular motion

In uniform circular motion the speed is constant but the velocity changes direction, so the body is accelerating. The centripetal acceleration is $a=\frac{v^2}{r}$ directed to the centre, and the centripetal force is $F=\frac{m{v}^2}{r}$. Centrifugal force is the apparent outward force felt in a rotating frame. Examples of centripetal force: the tension in a string, gravitation for planets, friction for a car on a bend.

Projectile motion

A projectile launched at angle $\theta$ with speed $u$ has: time of flight $T=\frac{2u\sin \theta }{g}$, maximum height $H=\frac{u^2{\sin }^2\theta }{2g}$, range $R=\frac{u^2\sin 2\theta }{g}$. The range is maximum at 45° and is the same for angles $\theta$ and $90°-\theta$.

Acids

An acid is a substance that gives hydrogen ions (H⁺) (hydronium ions, H₃O⁺) in water. Acids are sour in taste, turn blue litmus red, and react with metals, carbonates and bases.

Properties

• Acid + metal → salt + hydrogen: $\text{Zn}+{\text{H}}_2{\text{SO}}_4\to {\text{ZnSO}}_4+{\text{H}}_2$. (The hydrogen gas burns with a "pop" sound.)
• Acid + metal carbonate/bicarbonate → salt + water + carbon dioxide (brisk effervescence; the gas turns lime water milky).
• Acid + base → salt + water (neutralisation).
• Acids conduct electricity in solution, since they produce ions.
• Concentrated acids are corrosive; dilute an acid by adding the acid slowly to water (never water to acid), since the process gives out a lot of heat.

Common acids

Basicity: the number of replaceable H⁺ ions: HCl (monobasic), H₂SO₄ (dibasic), H₃PO₄ (tribasic).

Bases and alkalis

A base gives hydroxide ions (OH⁻) in water, or accepts H⁺. A base soluble in water is an alkali (NaOH, KOH, Ca(OH)₂, NH₄OH). Bases are bitter, feel soapy, turn red litmus blue, and conduct electricity in solution.

• Base + acid → salt + water.
• Base + ammonium salts liberates ammonia.
• Strong alkalis are corrosive.

Common bases

Antacids (sodium bicarbonate, magnesium hydroxide, aluminium hydroxide) relieve the excess acid in the stomach.

Indicators

An indicator changes colour in acid or alkaline solution.

Olfactory indicators: onion, vanilla and clove oils lose their smell in a base.

The pH scale

The pH is a measure of the hydrogen-ion concentration: $\text{pH}=-{\log }_{10}[{\text{H}}^{+}]$. The scale runs from 0 to 14:

A change of one pH unit corresponds to a tenfold change in $[{\text{H}}^{+}]$. The pH is measured with pH paper or a pH meter.

Acid rain has a pH below 5.6, caused by sulphur dioxide and nitrogen oxides; it damages buildings (the Taj Mahal), plants and aquatic life.

pH in daily life

• Tooth decay starts when the pH in the mouth falls below about 5.5; toothpastes are basic and neutralise the acid.
• Soil pH decides plant growth: acidic soils are treated with lime; alkaline soils with gypsum or organic matter.
• Indigestion is due to excess HCl in the stomach and is relieved by antacids.
• Bee sting (methanoic acid) is treated with baking soda; a wasp sting (alkaline) with vinegar.
• The pH of blood is maintained by buffers.

Overview

The human body is organised as cells → tissues → organs → organ systems. Each system does a specific job, but all work together to maintain homeostasis (a steady internal environment).

Digestive system

Digestion is the breakdown of complex food into simple, absorbable substances.

Alimentary canal: mouth → pharynx → oesophagus → stomach → small intestine (duodenum, jejunum, ileum) → large intestine (colon, rectum) → anus. Associated glands: salivary glands, liver, pancreas.

• Carbohydrates → glucose; proteins → amino acids; fats → fatty acids and glycerol.
• The appendix is a small vestigial organ at the junction of the small and large intestines.
• Enzymes: biological catalysts (proteins) that speed up reactions; work at specific pH and temperature (pepsin: acidic; trypsin: alkaline).
• Ptyalin — mouth; pepsin — stomach; trypsin, lipase, amylase — pancreas; lactase — small intestine (lactose intolerance).

Respiratory system

• Path of air: nose → pharynx → larynx (voice box; contains the vocal cords) → trachea (windpipe, supported by C-shaped cartilage rings) → bronchi → bronchioles → alveoli (tiny air sacs; exchange of gases takes place here; about 300–500 million in the lungs).
• The diaphragm and intercostal muscles help breathing. Inhalation: the diaphragm contracts and moves down, ribs go up and out; exhalation is the reverse.
• Breathing rate: about 12–20 times per minute at rest. Oxygen is carried by haemoglobin; most carbon dioxide is carried as bicarbonate in plasma.
• Air composition: inhaled — about 21 % O₂, 0.04 % CO₂; exhaled — about 16 % O₂ and about 4 % CO₂.
• Respiration at the cellular level (cellular respiration): $\text{glucose}+\text{oxygen}\to {\text{CO}}_2+\text{water}+\text{energy (ATP)}$ occurs in mitochondria. Anaerobic respiration (without oxygen) gives lactic acid in muscles (cramps) and ethanol + CO₂ in yeast.
• Diseases: asthma (narrowing of bronchioles), pneumonia, tuberculosis (TB), bronchitis, emphysema, silicosis and asbestosis (occupational).

Circulatory system

• Heart: a muscular organ, about the size of a fist, located slightly left in the chest; weighs about 300 g; has four chambers — two atria (upper, receive blood) and two ventricles (lower, pump blood). The left ventricle has the thickest wall (pumps blood to the whole body). The right side carries deoxygenated blood to the lungs; the left side carries oxygenated blood to the body. Valves prevent backflow. Normal heart rate is about 72 beats per minute at rest; normal blood pressure is about 120/80 mm Hg (systolic/diastolic), measured with a sphygmomanometer. The natural pacemaker is the sino-atrial (SA) node. ECG records the heart's electrical activity.
• Double circulation: blood passes twice through the heart in one full circuit (pulmonary circulation: heart → lungs → heart; systemic circulation: heart → body → heart).
• Blood vessels: arteries (carry blood away from the heart; thick, elastic walls; the pulmonary artery carries deoxygenated blood), veins (carry blood to the heart; thin walls, valves; the pulmonary vein carries oxygenated blood), capillaries (thin; exchange of materials).
• Blood (about 5–6 litres in an adult; 7–8 % of body weight):

• Blood groups (ABO system, Karl Landsteiner, 1901): A, B, AB, O. O is the universal donor, AB is the universal recipient. The Rh factor (Rhesus) is present (Rh⁺) or absent (Rh⁻). Rh incompatibility can affect a second pregnancy (a mother Rh⁻ and a foetus Rh⁺).
• Haemoglobin low → anaemia (iron deficiency). Normal Hb: about 13–17 g/dL in men, 12–15 g/dL in women. Haemophilia (blood does not clot; a sex-linked genetic disorder).
• Lymphatic system: lymph, lymph nodes, spleen, and thymus; helps in immunity and returns fluid to the blood.
• The spleen is the largest lymphatic organ. Heart attack (myocardial infarction) results from a blocked coronary artery; atherosclerosis is the hardening/blocking of arteries by cholesterol.