Fundamental and Derived Quantities, SI Units and Conversions for SS 1

Fundamental and Derived Quantities and Units

Performance Objectives

By the end of the lesson, students should be able to:

1. differentiate between fundamental and derived quantities;
2. convert units from m.k.s to SI unit;
3. identify different simple measuring instruments like meter rule, stop watch, spring balance, etc.;
4. use meter rule, balances, stop watch, etc., to measure some physical quantities.

Introduction to Physical Quantities

In Physics, we study the natural world and try to understand how it works. To do this, we often need to measure things. Anything that can be measured is called a physical quantity. Examples of physical quantities include length, mass, time, temperature, speed, and volume.

For any measurement to be meaningful, it must have both a numerical value and a unit. For instance, saying “the length is 5” is incomplete. It should be “the length is 5 metres” or “5 centimetres”. The unit tells us what standard the measurement is being compared to.

Fundamental Quantities and Units

Fundamental quantities are the basic physical quantities that cannot be expressed in terms of other physical quantities. They are independent of each other and form the foundation upon which all other physical quantities are built.

The units used to measure fundamental quantities are called fundamental units.

The curriculum specifies the following fundamental quantities for SS1:

1. Mass: Mass is a measure of the amount of matter in an object. It is a fundamental property of an object and does not change with location.

   The SI unit of mass is the kilogram (kg).

2. Length: Length is a measure of distance or extent in space. It can refer to height, width, depth, or the distance between two points.

   The SI unit of length is the metre (m).

3. Time: Time is a measure of duration or the interval between two events. It helps us sequence events and understand how long processes take.

   The SI unit of time is the second (s).

4. Electric Charge: Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. It can be positive or negative.

   The SI unit of electric charge is the Coulomb (C).

Derived Quantities and Units

Derived quantities are physical quantities that are obtained by combining two or more fundamental quantities through multiplication or division. They are dependent on fundamental quantities.

The units used to measure derived quantities are called derived units. These units are also formed by combining fundamental units.

Examples of derived quantities and their units include:

1. Area: Area is the measure of the extent of a two-dimensional surface. It is calculated by multiplying two lengths.

   The unit of area is metre × metre = square metre (m²).

2. Volume: Volume is the measure of the amount of space occupied by a three-dimensional object. It is calculated by multiplying three lengths.

   The unit of volume is metre × metre × metre = cubic metre (m³).

3. Speed: Speed is the rate at which an object moves. It is calculated by dividing distance (length) by time.

   The unit of speed is metre / second = metre per second (m/s).

4. Density: Density is the measure of mass per unit volume. It is calculated by dividing mass by volume.

   The unit of density is kilogram / cubic metre = kilogram per cubic metre (kg/m³).

5. Acceleration: Acceleration is the rate of change of velocity (speed in a given direction). It is calculated by dividing speed by time.

   The unit of acceleration is (metre per second) / second = metre per second squared (m/s²).

The International System of Units (SI)

The International System of Units, abbreviated as SI (from the French “Système International d’Unités”), is the modern form of the metric system and is the most widely used system of measurement in the world. It provides a consistent and standardised way to measure physical quantities, which is crucial for scientific communication and trade.

The SI system is built upon a set of seven base units, from which all other units are derived. For mechanical quantities, the base units are the metre (m) for length, the kilogram (kg) for mass, and the second (s) for time. This is often referred to as the m.k.s system, which forms the core of SI for these quantities.

When we talk about converting units from “m.k.s to SI unit,” it means ensuring that all measurements are expressed using the standard SI base units (metre, kilogram, second, Coulomb, etc.) or their derived forms. This often involves converting between different prefixes (like centi-, milli-, kilo-) or converting units from other systems into the SI system.

Converting Units

Unit conversion is the process of changing a measurement from one unit to another without changing its value. This is important for calculations where all quantities must be in consistent units, typically SI units.

To convert units, we use conversion factors. A conversion factor is a ratio of two equivalent measurements expressed in different units. For example, since 1 metre is equal to 100 centimetres, the conversion factor can be written as (1 m / 100 cm) or (100 cm / 1 m).

Steps for Unit Conversion:

1. Identify the unit you have and the unit you want to convert to.
2. Find the appropriate conversion factor(s) that relate these units.
3. Multiply the given measurement by the conversion factor(s) in such a way that the original unit cancels out, leaving the desired unit.

Worked Examples of Unit Conversion:

Example 1: Converting Length

Convert 250 centimetres (cm) to metres (m).

1. Given: 250 cm. Desired: m.
2. Conversion factor: 1 m = 100 cm. So, (1 m / 100 cm).
3. Calculation:

250 cm × (1 m / 100 cm) = (250 / 100) m = 2.5 m

Therefore, 250 cm is equal to 2.5 m.

Example 2: Converting Mass

Convert 500 grams (g) to kilograms (kg).

1. Given: 500 g. Desired: kg.
2. Conversion factor: 1 kg = 1000 g. So, (1 kg / 1000 g).
3. Calculation:

500 g × (1 kg / 1000 g) = (500 / 1000) kg = 0.5 kg

Therefore, 500 g is equal to 0.5 kg.

Example 3: Converting Speed

Convert 72 kilometres per hour (km/h) to metres per second (m/s).

1. Given: 72 km/h. Desired: m/s.
2. Conversion factors:
   1. For length: 1 km = 1000 m. So, (1000 m / 1 km).
   2. For time: 1 hour = 60 minutes = 60 × 60 seconds = 3600 s. So, (1 h / 3600 s).
3. Calculation:

72 km/h = 72 (km / h)

= 72 × (1000 m / 1 km) × (1 h / 3600 s)

= (72 × 1000) / 3600 m/s

= 72000 / 3600 m/s

= 20 m/s

Therefore, 72 km/h is equal to 20 m/s.

Measuring Instruments

To measure physical quantities accurately, various instruments are used. Identifying and knowing how to use these instruments is a key skill in Physics.

1. Meter Rule

   A meter rule is a common instrument used for measuring length or distance. It is typically one metre long and marked in centimetres (cm) and millimetres (mm).

   The smallest division on a standard meter rule is usually 1 millimetre (0.1 cm).

2. Stopwatch

   A stopwatch is used to measure intervals of time. It can be mechanical (analogue) or digital. Digital stopwatches are generally more precise and easier to read.

   Stopwatches are commonly used in experiments to measure the duration of events, such as the time taken for an object to fall or for a pendulum to complete a swing.

3. Spring Balance

   A spring balance is used to measure force or weight. It works on the principle that the extension of a spring is directly proportional to the force applied to it (Hooke’s Law, which will be studied in more detail later). The scale is usually calibrated in Newtons (N) or kilograms-force (kgf).

   When an object is hung from the hook of a spring balance, the spring stretches, and a pointer indicates the reading on the scale.

4. Chemical Balance (or Beam Balance)

   A chemical balance, also known as a beam balance, is used to measure mass accurately. It works by comparing the unknown mass of an object with known standard masses (weights).

   The object to be weighed is placed on one pan, and standard masses are added to the other pan until the beam is balanced, indicating equal masses on both sides.

Measuring Physical Quantities Using Instruments

How to Measure Length Using a Meter Rule

The meter rule is used to measure the length of objects or distances. Accurate measurement requires careful handling and observation.

The procedure involves the following steps:

1. Place the object: Place the meter rule along the object whose length is to be measured. Ensure one end of the object aligns with the zero mark of the rule.
2. Read the scale: Look at the other end of the object and read the mark on the meter rule that aligns with it.
3. Avoid parallax error: Position your eye directly above the mark being read to avoid parallax error. Parallax error occurs when the eye is not perpendicular to the scale, leading to an incorrect reading.
4. Record the reading: Note down the reading, including the unit (e.g., 35.7 cm or 0.357 m).

How to Measure Time Using a Stopwatch

A stopwatch is used to measure the duration of an event.

The procedure involves the following steps:

1. Reset the stopwatch: Before starting, ensure the stopwatch is reset to zero.
2. Start timing: Press the ‘start’ button precisely at the beginning of the event.
3. Stop timing: Press the ‘stop’ button precisely at the end of the event.
4. Read and record: Read the time displayed on the stopwatch and record it, usually in seconds (s).
5. Repeat measurement: For better accuracy, repeat the measurement several times and calculate the average.

How to Measure Mass Using a Chemical Balance

A chemical balance is used for accurate measurement of mass.

The procedure involves the following steps:

1. Level the balance: Ensure the balance is placed on a level surface and adjusted so that the pointer is at the zero mark when both pans are empty.
2. Place the object: Carefully place the object whose mass is to be measured on the left pan.
3. Add standard masses: Place known standard masses (weights) on the right pan, starting with larger masses and gradually adding smaller ones, until the pointer returns to the zero mark.
4. Sum the masses: Add up the values of all the standard masses on the right pan. This sum represents the mass of the object.
5. Handle masses carefully: Always use forceps to handle standard masses to avoid adding dirt or oils from hands, which can affect accuracy.

How to Measure Weight/Force Using a Spring Balance

A spring balance measures the weight of an object, which is a type of force.

The procedure involves the following steps:

1. Check zero reading: Hold the spring balance vertically and ensure the pointer is at the zero mark when nothing is attached to the hook. If it is not, adjust it if possible, or note the zero error.
2. Attach the object: Carefully hang the object whose weight is to be measured from the hook of the spring balance.
3. Read the scale: Once the spring has stopped oscillating and the pointer is steady, read the value indicated by the pointer on the scale.
4. Record the reading: Note down the reading, including the unit (e.g., 15 N).