← back
unit 1
1.1 physical quantities 1.2 motion 1.3 mass & weight 1.4 density 1.5 forces 1.6 momentum 1.7 energy, work & power 1.8 pressure
1.1

physical quantities and measurement

measurements

measuring length

use a ruler to measure lengths. place the object along the scale with the zero mark at one end. read the measurement at the other end. always read perpendicular to the scale to avoid parallax error.

measuring volume

use a measuring cylinder to find the volume of liquids or irregular solids. read the volume at the bottom of the meniscus (curved surface) with your eye level with the scale to avoid parallax error.

measuring time

use a clock or digital timer to measure time intervals. a stopwatch is accurate to about 0.01 s. for short, repeating events (like a pendulum swing), measure the time for multiple cycles and divide by the number of cycles to reduce error.

scalar quantities

have magnitude (size) only. no direction needed. examples: distance, speed, time, mass, energy, temperature.

vector quantities

have magnitude and direction. direction is essential to describe them fully. examples: force, weight, velocity, acceleration, momentum, electric field strength, gravitational field strength.

finding resultant vectors

the resultant is the single vector that has the same effect as two or more vectors combined. for two vectors at right angles, use the pythagorean theorem:

R² = A² + B²

alternatively, draw the vectors to scale on graph paper, place them head-to-tail, and measure the resultant from the start of the first vector to the end of the second.

parallax error

reading an instrument at an angle rather than straight on. the value appears to shift depending on viewing angle.

  • read measuring cylinders at eye level with the meniscus
  • read rulers perpendicular to the scale
  • read analogue meters from directly in front

parallax error is systematic – it cannot be removed by averaging. you must use correct technique.

systematic error

error that shifts all measurements in one direction (consistently too high or too low).

  • zero error: thermometer reads 0.2°c in ice
  • parallax: always reading a scale from the side
  • calibration: a ruler has shrunk slightly

differs from random error (scattered readings). averaging does not reduce systematic error – you must fix the cause.

measurement uncertainty

every measurement has limits to its precision. a ruler's smallest division is 1 mm, so uncertainty is ±0.5 mm. record measurements to match your instrument's precision.

significant figures

  • all non-zero digits are significant (2.5 = 2 sig figs)
  • zeros between non-zero digits are significant (2.05 = 3 sig figs)
  • leading zeros are not significant (0.025 = 2 sig figs)
  • trailing zeros after decimal point are significant (2.50 = 3 sig figs)