Physical Quantities and units | Physics for Grade 10 PDF Download

What is a Physical Quantity?

• Speed and velocity are examples of physical quantities; both can be measured
• All physical quantities consist of a numerical magnitude and a unit
• In physics, every letter of the alphabet (and most of the Greek alphabet) is used to represent these physical quantities
• These letters, without any context, are meaningless
• To represent a physical quantity, it must contain both a numerical value and the unit in which it was measured
• The letter v be used to represent the physical quantities of velocity, volume or voltage
• The units provide the context as to what v refers to
  • If v represents velocity, the unit would be m s^–1
  • If v represents volume, the unit would be m³
  • If v represents voltage, the unit would be V

All physical quantities must have a numerical magnitude and a unit

Estimating Physical Quantities

• There are important physical quantities to learn in physics
• It is useful to know these physical quantities, they are particularly useful when making estimates
• A few examples of useful quantities to memorise are given in the table below (this is by no means an exhaustive list)

Estimating Physical Quantities Table

Example: Estimate the energy required for an adult man to walk up a flight of stairs.

SI Units

• There is a seemingly endless number of units in Physics
• These can all be reduced to six base units from which every other unit can be derived
• These seven units are referred to as the SI Base Units; this is the only system of measurement that is officially used in almost every country around the world

SI Base Quantities Table

Derived Units

• Derived units are derived from the seven SI Base units
• The base units of physical quantities such as:
  • Newtons, N
  • Joules, J
  • Pascals, Pa, can be deduced
• To deduce the base units, it is necessary to use the definition of the quantity
• The Newton (N), the unit of force, is defined by the equation:
  • Force = mass × acceleration
  • N = kg × m s^–2 = kg m s^–2
  • Therefore, the Newton (N) in SI base units is kg m s^–2
• The Joule (J), the unit of energy, is defined by the equation:
  • Energy = ½ × mass × velocity²
  • J = kg × (m s^–1)² = kg m² s^–2
  • Therefore, the Joule (J) in SI base units is kg m² s^–2
• The Pascal (Pa), the unit of pressure, is defined by the equation:
  • Pressure = force ÷ area
  • Pa = N ÷ m² = (kg m s^–2) ÷ m² = kg m^–1 s^–2
  • Therefore, the Pascal (Pa) in SI base units is kg m^–1 s^–2

Homogeneity of Physical Equations

• An important skill is to be able to check the homogeneity of physical equations using the SI base units
• The units on either side of the equation should be the same
• To check the homogeneity of physical equations:
  • Check the units on both sides of an equation
  • Determine if they are equal
  • If they do not match, the equation will need to be adjusted

How to check the homogeneity of physical equations

Powers of Ten

• Physical quantities can span a huge range of values
• For example, the diameter of an atom is about 10^–10 m (0.0000000001 m), whereas the width of a galaxy may be about 10²¹ m (1000000000000000000000 m)
• This is a difference of 31 powers of ten
• Powers of ten are numbers that can be achieved by multiplying 10 times itself
• It is useful to know the prefixes for certain powers of ten

Powers of Ten Table

Scalars & Vectors

What are Scalar & Vector Quantities?

• A scalar is a quantity which only has a magnitude (size)
• A vector is a quantity which has both a magnitude and a direction
• For example, if a person goes on a hike in the woods to a location which is a couple of miles from their starting point
  • As the crow flies, their displacement will only be a few miles but the distance they walked will be much longer

Displacement is a vector while distance is a scalar quantity

• Distance is a scalar quantity because it describes how an object has travelled overall, but not the direction it has travelled in
• Displacement is a vector quantity because it describes how far an object is from where it started and in what direction
• There are a number of common scalar and vector quantities

Scalars and Vectors Table

Combining Vectors

• Vectors are represented by an arrow
  • The arrowhead indicates the direction of the vector
  • The length of the arrow represents the magnitude
• Vectors can be combined by adding or subtracting them from each other
• There are two methods that can be used to combine vectors: the triangle method and the parallelogram method
• To combine vectors using the triangle method:
  • Step 1: link the vectors head-to-tail
  • Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector
• To combine vectors using the parallelogram method:
  • Step 1: link the vectors tail-to-tail
  • Step 2: complete the resulting parallelogram
  • Step 3: the resultant vector is the diagonal of the parallelogram
• When two or more vectors are added together (or one is subtracted from the other), a single vector is formed and is known as the resultant vector

Vector Addition

Vector Subtraction

Condition for Equilibrium

• Coplanar forces can be represented by vector triangles
• In equilibrium, these are closed vector triangles. The vectors, when joined together, form a closed path

If three forces acting on an object are in equilibrium; they form a closed triangle

Resolving Vectors

• Two vectors can be represented by a single resultant vector that has the same effect
• A single resultant vector can be resolved and represented by two vectors, which in combination have the same effect as the original one
• When a single resultant vector is broken down into its parts, those parts are called components
• For example, a force vector of magnitude F and an angle of θ to the horizontal is shown below

• It is possible to resolve this vector into its horizontal and vertical components using trigonometry

• For the horizontal component, F_x = Fcosθ
• For the vertical component, F_y = Fsinθ