FLASH CARDS: UNITS & DIMENSIONS

Two parts of every measurement in physics

A number (n) and a unit (u). Example: 40 cm (40 is n, cm is u).

Q = n × u

The quantity (Q) equals the number (n) times the unit (u). The unit shows what you’re measuring, the number shows how much.

Importance of units in physics

Units give meaning to numbers. Without units, '40' could mean 40 seconds, 40 dollars, or 40 elephants! Always write the unit.

C.G.S. system

Centimeter-Gram-Second system. Length = centimeter (cm), Mass = gram (g), Time = second (s).

F.P.S. system

Foot-Pound-Second system. Length = foot (ft), Mass = pound (lb), Time = second (s).

M.K.S. system

Meter-Kilogram-Second system. Length = meter (m), Mass = kilogram (kg), Time = second (s).

S.I. system

International System of Units—an improved version of the M.K.S. system. It’s the global standard in science.

Fundamental quantities in S.I. units

Length: meter (m), Mass: kilogram (kg), Time: second (s), Electric current: ampere (A), Temperature: kelvin (K), Light intensity: candela (cd), Amount of substance: mole (mol).

Derived quantities

Quantities calculated from fundamental ones (like speed = distance/time). Their units are made from combinations of base units.

Purpose of metric prefixes

They show multiples or fractions of a unit (powers of ten). Example: kilometer (km) = 1,000 meters.

Metric prefixes and their powers of ten

kilo- (k): 10^3 = 1,000, centi- (c): 10^{-2} = 0.01, milli- (m): 10^{-3} = 0.001, micro- (μ): 10^{-6} = 0.000001, nano- (n): 10^{-9} = 0.000000001.

Converting from kg to mg

Move 6 decimal places right (kilo to milli: 3 for kilo, 3 for milli, total = 6). Example: 1 kg = 1,000,000 mg.

Converting from cm to m

Move 2 decimal places left (centi to base unit). Example: 2.3 cm = 0.023 m.

Unit for mass in SI

Kilogram (kg).

Unit for time in SI

Second (s).

Three main systems of units

C.G.S.: cm, g, s; M.K.S.: m, kg, s; F.P.S.: ft, lb, s.

Metric prefixes from largest to smallest

Larger: exa (E), peta (P), tera (T), giga (G), mega (M), kilo (k); Smaller: deci (d), centi (c), milli (m), micro (μ), nano (n), pico (p), femto (f), atto (a).

Analogy for metric prefixes

Think of metric prefixes like zooming in and out with a camera: 'Kilo-' is zoomed far out (big picture, 1,000× bigger); 'Milli-' is zoomed way in (tiny details, 1,000× smaller). Each 'step' on the prefix map is like zooming in/out by 10×!