# Physical Quantities

Introduction to physics is the first chapter of SPM form 4 physics. It is one of the most important topics in SPM physics for what you learn in this topic is very useful in other topics.

There are 4 main sub-topics in this chapter:

1. Physical quantity,
2. Measurement,
3. Measuring instrument and
4. Scientific investigation.

### Physical Quantity

A physical quantity is a quantity that can be measured. Physical quantities can be divided into 2 types: the base quantities and the derived quantities.

In this lesson, we will focus on the classification of physical quantities. We will discuss 2 ways of classification. In classification 1, we divide physical quantities to base and derived quantities. For base quantities, we will discuss the 5 base quantities and their SI unit. For derived quantities, we will discuss how to find derived unit and the unit of a constant in a physics formula. We will also learn how to find the base quantities in a derived quantity.

In classification 2, we divide physical quantities into scalar quantities and vector quantities. We will discuss what scalar quantities are and what vector quantities are.

### Base Quantities

A base quantity is a quantity that cannot be defined in any other physical quantities.

 Quantity SI Unit Symbol of Unit Length metre m Mass kilogram kg Time second s Electric current Ampere A Temperature Kelvin K

The table shows the 5 base quantities and their SI units. They are length, mass, time, electric current and temperature. Take notes that the SI unit of current is Ampere and the SI unit of temperature is Kelvin but not degree Celsius. In SPM, you need to memorise all the 5 base quantities and their units.

### Derived Quantities

A derived quantity is a physical quantity that is not a base quantity. It is the quantities which derived from the base quantities through multiplication or division.

For example, area of a rectangle can be calculated by multiplying the length of the rectangle by the width of the rectangle. Both the length and the width are base quantities. Multiplication of these 2 base quantities produces area, Therefore, area is a derived quantity. In other words, area is derived from the base quantity, length.

Let’s see another example. Speed is equal to distance over time. Distance is a base quantity. Time is also a base quantity.  Division of distance by time produces speed, hence speed is a derived quantity. Derived quantities are the quantities which derived from the base quantities through multiplication or division.

##### More examples of derived quantities

One of the question that students always ask is, “Do I need to memorise all of this?”  and the answer is, “It’s up to you.”

You will learn all these equations in other topics. For example, you will learn frequency in Wave, density in Force and Pressure, velocity in Force and Motion and ect. Which means, if you do not memorise it now, you can still learn them in other topics, and it’s much easier to learn it in their particular topic rather than merely memorising here.

However, some questions related to these equations may still come out in your physics test, which will cause you losing a few marks, if you don’t memorise it now.

##### Derived Unit

A derived unit is the unit of a derived quantities. It can be determined from the equation of the derived quantity.

For example, speed is equal to distance over time. The unit of distance is metre, whereas the unit of time is second. Therefore, the unit of speed is metre over second, which is equal to metre per second or ms-1. The unit s-1 is the symbol of 1/s in index form. In physics, usually the units are written in index form.

Let’s see another example. Acceleration is equal to velocity over time. The unit of velocity is m/s whereas the unit of time is second. Therefore, the unit of acceleration is m/s over s, which equal to metre per second per second, or ms-2.

Example 1 – Finding Derived Unit

The moment inertia (I) of a disc is given by the following equation: I = 1/2mr2 where m = mass of the disc and r = radius. Find the unit of moment inertia, I.

m is mass and its SI unit is kilogram (kg). r is the radius, which is length. Therefore the unit is metre (m). The ½ has no unit. From the equation I = ½ mr2, the unit of moment inertia I equal to kg x m2, which equal to kilogram metre square.

Example 2 – Finding the Unit of a Constant.

The relationship of the mass of a metal plat with its area is given by the equation: mass = k ´ area where k is a constant. What is the unit of k?

Mass = k x area, hence k = mass/area.

The unit of mass is kg whereas the unit of area is m2.

As the result, the unit of k = kg/ m2, which is equal to kg m-2.

Derived quantities and their unit can be separated into their respective base quantities and base units.

For example, the unit of force is Newton. Force is also given by the equation force equal to mass × acceleration. The SI unit of mass is kg and the unit of acceleration is ms-2. Therefore the unit of force is also equal to kg ms-2. As a conclusion, 1 N is equal to 1 kg ms-2. N is the SI unit of force, whereas kg ms-2 is the SI base unit of force.

Example 3

Convert the following derived unit to their appropriate base unit:

1. Coulomb (C)
2. Pascal (Pa)

Notes: Coulomb is the unit of charge. The equation of charge is: Charge = Current x Time. Pascal is the unit of pressure. The equation of pressure is: Pressure = Force/Area

Coulomb is the SI unit of electric charge. In equation, charge is equal to current x time. The unit of current is Ampere (A) whereas the unit of time is second. Therefore, we conclude that the unit of electric charge, Coulomb = Ampere second.

Pascal is the SI unit of pressure. In equation, we write Pressure = Force over area. The unit of force is Newton and the unit of area is metre square.

However, Newton is not yet a base unit, hence we need to find the SI base unit which equivalent to Newton.

Force = Mass x acceleration. The unit of mass is kg whereas the unit of acceleration is ms-2. Therefore, Newton is equal to kg ms-2.

Substitute this into the equation, we get Pa = kg ms-2 / m2. Simplify the equation, we get Pa = kg m-1 s-2.