DU Ka Unit (Science Unit) flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Newton's Second Law

The net force on an object equals its mass multiplied by its acceleration, written F = ma, with force in newtons, mass in kilograms and acceleration in metres per second squared.

Work-Energy Theorem

The total work done by all forces on a body equals the change in its kinetic energy, so W = ½mv² − ½mu² for mass m moving from speed u to speed v.

Ohm's Law

For a conductor at constant temperature, the potential difference across it equals current times resistance, V = IR, with V in volts, I in amperes and R in ohms.

Lens Equation

The thin lens relation 1/f = 1/v + 1/u links focal length f, image distance v and object distance u; magnification is m = v/u using consistent sign conventions.

Wave Speed Relation

Wave speed equals frequency multiplied by wavelength, v = fλ. When a wave enters a new medium its speed and wavelength change but its frequency stays the same.

Ideal Gas Law

For an ideal gas, pressure times volume equals moles times the gas constant times absolute temperature, PV = nRT, with R about 8.314 J/(mol·K).

Mole Concept

One mole of any substance contains 6.022 × 10²³ particles, and the number of moles equals the mass of the sample divided by its molar mass.

Molarity

Molarity is the number of moles of solute per litre of solution. During dilution the moles stay constant, so M₁V₁ = M₂V₂.

pH Scale

pH is the negative base-ten logarithm of hydrogen ion concentration. At 25 °C, pH plus pOH equals 14, and a neutral solution has pH 7.

Oxidation and Reduction

Oxidation is loss of electrons and reduction is gain of electrons. In any redox reaction the total electrons lost equal the total electrons gained.

Le Chatelier's Principle

When a system at equilibrium is disturbed by a change in concentration, pressure or temperature, the equilibrium shifts in the direction that opposes the change.

Empirical Formula

The empirical formula shows the simplest whole-number ratio of atoms in a compound, while the molecular formula is that ratio multiplied by an integer.

Quadratic Formula

For ax² + bx + c = 0 with a not zero, the roots are x = [−b ± √(b² − 4ac)] / 2a, and the discriminant b² − 4ac determines their nature.

Sum and Product of Roots

For the quadratic ax² + bx + c = 0 with roots α and β, the sum α + β equals −b/a and the product αβ equals c/a.

Arithmetic Progression

A sequence with a constant common difference d. Its nth term is a + (n−1)d and the sum of n terms is n/2 times twice the first term plus (n−1)d.

Geometric Progression

A sequence with a constant ratio r. Its nth term is ar^(n−1), and the sum of n terms is a(rⁿ − 1)/(r − 1) when r is not 1.

Standard Derivatives

Common results: derivative of xⁿ is nx^(n−1), of sin x is cos x, of eˣ is eˣ, and of ln x is 1/x, all with respect to x.

Power Rule Integration

Integration reverses differentiation: the integral of xⁿ dx is x^(n+1)/(n+1) plus a constant, provided n is not equal to −1.

Pythagorean Identity

For any angle θ, sin²θ + cos²θ equals 1. Dividing through by cos²θ gives 1 + tan²θ = sec²θ, a useful simplification identity.

Addition Rule of Probability

For two events A and B, the probability of A or B equals P(A) + P(B) − P(A and B), subtracting the overlap counted twice.

Photosynthesis Equation

In chloroplasts, six carbon dioxide molecules and six water molecules plus light energy produce one glucose molecule and six oxygen molecules released as gas.

Cellular Respiration

Glucose plus oxygen yields carbon dioxide, water and ATP energy. Glycolysis occurs in the cytoplasm, and most ATP comes from the mitochondria.

DNA Base Pairing

In DNA, adenine pairs with thymine and guanine pairs with cytosine. In RNA, uracil replaces thymine, pairing with adenine instead.

Law of Segregation

Mendel's law states that the two alleles of a gene separate during gamete formation, so each gamete carries only one allele of each gene.

Mitosis versus Meiosis

Mitosis produces two genetically identical diploid cells for growth and repair, while meiosis produces four haploid gametes with new allele combinations.

ABO Blood Groups

Alleles A and B are codominant and O is recessive, giving groups A, B, AB and O. Group O negative blood is the universal donor.

Enzyme Function

Enzymes are protein catalysts that lower the activation energy of a reaction, speeding it up without being consumed or permanently changed by it.

Harmonic Mean Speed

When equal distances are covered at speeds a and b, the average speed is the harmonic mean 2ab/(a + b), not the simple arithmetic average.

Successive Percentage Change

Two successive changes of x percent and y percent give a net change of x + y + xy/100 percent, which is not simply the sum of the two.

Combined Work Formula

If worker A alone finishes a job in a days and B alone in b days, working together they finish it in ab/(a + b) days.

Compound Interest Formula

The amount after T years is P(1 + R/100)^T, where P is the principal and R the annual rate, with interest compounded each year.

Clock Angle Formula

The angle between the hands is the absolute value of 30H − 5.5M degrees, where H is the hour and M the minute shown.