Introduction to Physical Quantities
Definition: Physical quantities are specific types of information about the world that we can measure using tools like rulers, clocks, thermometers, or scales. These measurements help us describe how objects behave or interact.
Importance: Physical quantities are very important because they allow scientists, engineers, and everyone else to describe how things move, change, or react in the physical world. Without them, we couldn’t make sense of motion, heat, electricity, or even time.
Components: Every physical quantity is made up of two main parts. One part is the magnitude, which tells us how much there is (a number), and the other part is the unit, which tells us what kind of measurement it is (like meters for length or seconds for time).
Example: For instance, the mass of the Sun can be written as 1.989 × 10³⁰ kg. Here, 1.989 × 10³⁰ is the magnitude, and “kg” (kilograms) is the unit that shows this quantity is a measurement of mass.
Types of Physical Quantities
Main categories: All physical quantities fall into two groups: scalar quantities, which have only size or amount, and vector quantities, which have both size and a specific direction.
Scalar Quantities
Scalar definition: Scalar quantities are measurements that only tell us how much of something there is, but not the direction it points to.
Description: When we talk about scalars, we only need to mention a number and a unit—there’s no need to say which way it’s going.
Examples: Some common scalar quantities include distance (like 5 km), mass (like 10 kg), speed (like 60 km/h), time (like 2 hours), and temperature (like 37°C). Other examples are area, volume, density, energy, and work.
Operations: You can add, subtract, multiply, or divide scalar quantities just like regular numbers because they don’t depend on direction.
Applications: Scalar quantities are used in many situations, such as calculating how long a journey takes, how much energy is used, or how hot something is.
Vector Quantities
Vector definition: Vector quantities are types of measurements that give us more than just how much of something there is. They also tell us which direction it is going. So, to describe a vector, we need two things: the size of the measurement (called magnitude) and the direction it points. This makes vectors different from scalar quantities, which only have size and no direction.
Description: When you want to describe a vector, you have to mention three things: a number that tells how big it is, the unit (like meters or newtons), and the direction it is pointing. For example, you might say “50 N to the north” to describe a force, or “10 m/s downward” to describe how fast and in which way something is moving.
Examples: Some common examples of vector quantities include:
- Displacement: This means how far and in which direction something has moved from its starting point.
- Velocity: This is speed with a direction added. For instance, 60 km/h to the east is velocity, not just speed.
- Acceleration: This tells us how quickly the velocity of something is changing, and in which direction.
- Force: A push or pull that has strength and a direction.
- Weight: The force of gravity pulling on an object; it always points toward the center of the Earth.
- Momentum and Impulse: These are related to how things move and change motion, and both depend on direction as well as how fast and how heavy something is.
Calculations: Since vectors involve directions, we can’t just add them like simple numbers. We have to use special rules, such as drawing arrows or using angles. This is called vector addition. We often use diagrams to help us figure out the right answer, especially when the vectors point in different directions.
Resultant vectors: Sometimes more than one vector acts on an object at the same time. For example, two people pushing a box in different directions. To figure out the total effect on the box, we must combine all the vectors, both their sizes and directions. This new vector is called the resultant vector, and we usually calculate it using diagrams or math.
Base Quantities
Definition: Base quantities are the simplest, most basic types of measurements in science. They are like the foundation or building blocks for all other measurements. You cannot break them down into anything simpler.
Alternate name: Scientists also call these fundamental quantities because they form the base of the whole measurement system. We use them to define everything else that we measure.
Role: Every other type of measurement in science, such as speed, pressure, or energy, is created by combining these base quantities in different ways using formulas.
List of base quantities:
- Length (meter, m): This measures how long or far something is. For example, the length of a pencil or the distance between two towns.
- Mass (kilogram, kg): This tells us how much matter or “stuff” is in an object. For example, a watermelon might have a mass of 3 kg.
- Time (second, s): This measures how long something takes to happen. For instance, how many seconds it takes to run a race.
- Thermodynamic temperature (kelvin, K): This measures how hot or cold something is on an absolute scale, starting from absolute zero (the coldest possible temperature).
- Electric current (ampere, A): This measures how much electric charge flows through a wire or device in one second.
- Luminous intensity (candela, cd): This tells us how bright a light source is. A flashlight and a lamp can have different luminous intensities.
- Amount of substance (mole, mol): This measures how many tiny particles (like atoms or molecules) are in a sample of material.
Derived Quantities
Definition: Derived quantities are measurements that are made by combining two or more base quantities. These are not basic, but they are very useful because they help describe real-world things like area, speed, and pressure.
Formation: We create derived quantities by multiplying or dividing base quantities. For example, if you divide distance (a base quantity) by time (another base quantity), you get speed or velocity (a derived quantity).
Examples and formulas:
- Area: A = l² — This tells us how much flat space a surface covers. For example, the area of a rectangle is found by multiplying its length and width (unit: square meters, m²).
- Volume: V = l³ — This tells us how much space an object takes up. Like how much water a bottle can hold (unit: cubic meters, m³).
- Density: ρ = m/V — This is mass divided by volume. It tells us how heavy something is for its size (unit: kilograms per cubic meter, kg/m³).
- Velocity: v = l/t — Distance divided by time. It shows how fast something is moving in a certain direction (unit: meters per second, m/s).
- Acceleration: a = v/t = l/t² — This is the change in velocity over time. It shows how quickly something is speeding up or slowing down (unit: meters per second squared, m/s²).
- Force: F = ma — This means force equals mass times acceleration. It shows how strongly something is being pushed or pulled (unit: newton or N, which is kg·m/s²).
- Momentum: p = mv — This is mass times velocity. It shows how much motion an object has (unit: kg·m/s).
- Pressure: P = F/A — This is force divided by area. It tells us how much force is applied over a certain surface (unit: pascal or Pa).
- Energy/Work: W = F × l — This is force multiplied by distance. It shows how much energy is used to move something (unit: joule or J).
- Charge: Q = It — This is electric current multiplied by time. It tells us how much electric charge flows in a certain time (unit: coulomb or C).
S.I. Units and Prefixes
S.I. system: The Système International (or S.I.) is a system of measurement used all over the world, especially in science and engineering. It helps everyone use the same units so we can compare and share results easily.
Purpose: This system makes sure that scientists and people from different countries or professions can understand each other. It avoids confusion when doing experiments or talking about data.
Base unit linkage: Each of the base quantities we talked about earlier has its own unit in the S.I. system. For example, we measure length in meters (m), mass in kilograms (kg), and time in seconds (s).
Derived units: These are units made by combining base units. For instance, velocity is measured in meters per second (m/s), which combines the units for length and time.
Prefixes use: We often measure things that are either very large or very small. To help with that, we use prefixes. A prefix changes the size of the unit by multiplying it by a power of ten. This helps us write big or small numbers more easily.
Common prefixes:
- pico (p): One-trillionth = 10⁻¹² (really, really small)
- nano (n): One-billionth = 10⁻⁹
- micro (µ): One-millionth = 10⁻⁶
- milli (m): One-thousandth = 10⁻³
- centi (c): One-hundredth = 10⁻²
- deci (d): One-tenth = 10⁻¹
- deka (da): Ten times = 10¹
- hecto (h): One hundred times = 10²
- kilo (k): One thousand times = 10³
- mega (M): One million times = 10⁶
- giga (G): One billion times = 10⁹
- tera (T): One trillion times = 10¹²
- peta (P): Ten quadrillion times = 10¹⁵
Prefix examples: If you have 1 kilometre (km), that means you have 1,000 meters, because “kilo” means 1,000. If a stopwatch shows 1 millisecond (ms), that means the time is 0.001 seconds, because “milli” means one-thousandth.