Physics - Using S.I. units

Sep 5, 2026

Upload by Finn

Worksheet focuses on using S.I. units to solve physics problems and verify equation correctness through unit homogeneity. It introduces base quantities and derived quantities, showing how derived unit expressions come from base units. Learners practise working out missing units and unit symbols in a table, calculating units through equations, and checking whether both sides of key formulas match in overall units. Activities include speed, kinetic energy, charge, power, and gravitational field strength.

LanguageEnglish

CategoryExam

FormatPDF

Pages29

Reading Time1 h 13 min

AccessFree to download

Learning outcomes

Base and derived S.I. units

Worked example: unit of speed

Unit calculation practice table

Homogeneity of physical equations

Worked example: kinetic energy

Further homogeneity questions

Charge, power, and gravitational field strength

Background: the Système Internationale (S.I.)

Table 1: S.I. base units

Derived units from relationships

Using S.I. units Specification references • 2.1.2 a) b) c) d) • M0.1 Recognise and make use of appropriate units in calculations Learning outcomes After completing the worksheet you should be able to: • show knowledge and understanding of base and derived S. I. units • use equations to work out derived units • use base units to check homogeneity of equations. Introduction Base quantities are measured in base units. These are units that are not based on other units. For example, mass is measured in kilograms and length is measured in metres. Other quantities have units which are derived from the base quantities. For example, the unit of density (kg m–3) is derived from the kilogram and the metre. The first example shows you how to use an equation to work out the unit of a derived quantity. The second example shows you how to check that an equation is homogeneous or, in other words, that its units are balanced. Worked example Question What is the S. I. unit of speed? Answer Step 1 Identify the equation to use. Speed is defined as: distatinceme~~ ~~ttravakeenlled Step 2 Write the equation in terms of units. The S.I. unit of speed is defined as: unit~~ ~~ofunidtistaof~~ ~~tinceme~~ ~~ttraakveenlled Step 3 Select the appropriate S. I. base units. S. I. unit of distance = metre (m) S. I. unit of time = second (s) Step 4 Insert the S. I. base units into the equation. metre (m) S. I. unit of speed = = metre per second = m s–1 time taken (s) Question 1 Work out the missing units, unit symbols and names, equations, and quantities in this table. (1 mark for each correct answer) | Physical quantity | Equation used | Unit | Derived unit symbol and name | | --- | --- | --- | --- | | frequency | 1
time period | a | Hz hertz | | volume | length3 | b | – | | acceleration | velocity
time | c | – | | force | mass 􀁵 acceleration | kg m s–2 | d | | work and energy | force 􀁵 distance | e | J joule | | voltage | energy electric charge | J C–1 | f | | electrical resistance | g | VA–1 | h | | momentum | mass 􀁵 velocity | i | – | | impulse | force 􀁵 time | j | – | | k | force
area | l | Pa pascal | | m | n | kg m–3 | – | Worked example Question Check that the equation: kinetic energy = 12 m v2 is homogeneous. Answer Make sure you always state which side of the equation you are working on, left-hand side (LHS) or right-hand side (RHS) . Step 1 Start with the LHS. The unit of kinetic energy is the joule. Change this to base units. LHS: J = N m = kg m s–2 􀁵 m = kg m2 s–2 Step 2 Repeat Step 1 for the RHS. RHS: units of 12 m v2 are kg 􀁵 (m s–1)2 = kg m2 s–2 1 (The constant, , is a number with no units. ) 2 Step 3 Don’t forget to write your conclusion. LHS = RHS so the equation is homogeneous. We can’t tell that there is a 12 in the equation, so we cannot say that the equation is correct, only that it is homogeneous. Questions 2 Use base units to show the equation Q = I t for electric charge passing a point in time t, when the electric current is I, is homogeneous. (1 mark) 3 Use base units to show that the equation P = I V is homogeneous , where I is electric current, V is voltage, and P is power measured in watts (W) . (Hint: 1 W = 1 J s–1) (2 marks) 4 The Earth’s gravitational field strength, g = 9.81 N kg–1 , is also sometimes given as the acceleration due to gravity , g = 9.81 m s–2. Show that these units are equivalent. (1 mark) Maths skills links to other areas You may also need to check equations are homogeneous wherever they are used in the specification – examples can be found in Chapter 3 Motion, and Topic 4.8 Density and pressure. You can also use this method to help you decide whether you have remembered an equation correctly. Homogeneity of physical equations Specification references • 2.1.2 a) b) d) • M0. 1, M2.2 Introduction In physics, all physical quantities are defined by mathematical relationships ,

FAQs

What are base units and derived units in S.I. measurements?

Base units measure quantities that are not defined using other units (e.g., mass in kilograms, length in metres). Derived units are formed from base units through physical relationships (e.g., density in kg m⁻³).

How can you find the S.I. unit of a derived quantity like speed?

Use the defining equation for the quantity, then substitute the S.I. base units for each variable. Simplifying the result gives the derived unit (for speed, metres per second, m s⁻¹).

How do you check whether a physics equation is homogeneous?

Write units on both sides of the equation, convert to base units where needed, and compare the overall units. If LHS units equal RHS units, the equation is homogeneous.

Sep 5, 2026

Upload by Finn