Physical quantities and measurement techniques

In physics, every measurement is a 'physical quantity', which consists of two parts: a numerical value (its magnitude) and a unit. For example, in '10 metres', 10 is the magnitude and 'metres' is the unit. To ensure scientists worldwide can understand each other, a standard system called SI units (Système International d'Unités) is used. The base SI units for the three most common quantities are the metre(m) for length, the kilogram (kg) for mass, and the second(s) for time. Sometimes, a quantity is very large or very small, so we use prefixes to modify the unit. For example, 'kilo'(k) means 1000 times bigger, so 1 kilometre (km) is 1000 metres. 'Milli'(m) means 1000 times smaller, so 1 millimetre (mm) is 0.001 metres. It is crucial to convert all quantities into their base SI units before using them in most physics equations.

Length is a fundamental measurement of distance. For everyday lengths in the lab, a metre rule or a 30 cm ruler is used. These are typically marked in centimetres (cm) and millimetres (mm). To measure accurately, you must avoid parallax error. This is an apparent shift in the object's position due to viewing the scale from an angle. To prevent this, always position your eye directly above the marking on the scale. The precision of a standard ruler is to the nearest millimetre. To measure very small thicknesses accurately, like a single sheet of paper, you should measure the thickness of a large stack (e.g., 500 sheets) and then divide the total thickness by the number of sheets. Area is the measure of a two-dimensional surface, calculated from length measurements. For a rectangle, it is length × width.

Volume is the amount of three-dimensional space an object occupies. The method for measuring it depends on the object's state and shape. For liquids, a measuring cylinder is used. Pour the liquid in and take the reading from the scale. For water and most liquids, the surface curves downwards, forming a meniscus. Your eye should be level with the bottom of the meniscus to get an accurate reading. For a regular solid, like a rectangular block, you can calculate its volume by measuring its length (l), width (w), and height(h) with a ruler and using the formula V = l × w × h. For an irregular solid (like a stone), you must use the displacement method. Submerge the object in a measuring cylinder of water and measure the volume of the water displaced, which is equal to the object's volume. The volume is the difference between the final water level and the initial water level.

Time is measured using a stopwatch or stopclock, which can measure to a precision of 0.1 s or 0.01 s. However, the main source of error is human reaction time when starting and stopping the clock. This error can be significant for short time intervals. To improve the precision of a time measurement for a repeating event, like a swinging pendulum, you should measure the time for a large number of complete cycles (e.g., 20 or 50 swings) and then divide the total time by the number of cycles. This calculates the average time for one cycle, known as the period. This technique makes the reaction time error at the start and end a much smaller fraction of the total time measured, greatly increasing the accuracy of the result for the period. Another potential error is a zero error, where the stopwatch does not start from exactly zero. Always check and, if possible, reset the device before starting.

Mass is a measure of the amount of matter in an object. It is a fundamental property and does not change with location. The SI unit for mass is the kilogram (kg). In the lab, mass is measured using a top-pan balance. Before placing an object on the balance, you should press the 'tare' or 'zero' button to ensure it starts from zero. Density is a derived quantity that describes how much mass is packed into a given volume. An object made of a dense material (like lead) has a lot of mass in a small space, while an object of a low-density material (like foam) has little mass in the same space. It is calculated by dividing an object's mass by its volume. The SI unit for density is kilograms per cubic metre (kg/m³), but grams per cubic centimetre (g/cm³) is also commonly used.

To find the density of any object, you need to measure two quantities: its mass and its volume. The procedure combines the techniques learned in previous sections. For a regular solid (e.g., a metal cube): 1. Measure its mass using a top-pan balance. 2. Measure its length, width, and height using a ruler. 3. Calculate its volume using V = l × w × h. 4. Calculate density using ρ = m/V. For an irregular solid (e.g., a stone): 1. Measure its mass using a top-pan balance. 2. Find its volume using the displacement method with a measuring cylinder and water. 3. Calculate density using ρ = m/V. For a liquid: 1. Place an empty measuring cylinder on a top-pan balance and tare it (set to zero). 2. Pour the liquid into the measuring cylinder and record its mass. 3. Read the volume of the liquid from the cylinder's scale. 4. Calculate density using ρ = m/V.