Units are a way of measuring physical quantities, such as length, mass, time, and temperature. They allow us to compare the size of different quantities and to express these quantities in a standardized way.
There are two main systems of units: the International System of Units (SI), which is used globally, and the British System of Units (also known as the imperial system), which is used primarily in the United Kingdom and its former colonies.
In the SI, the basic units of length, mass, and time are the meter, kilogram, and second, respectively. Other units, such as the Newton (for force), the joule (for energy), and the watt (for power), are derived from these basic units.
In the British system, the basic units of length, mass, and time are the foot, pound, and second, respectively. Other units, such as the pound-force (for force), the foot-pound (for energy), and the horsepower (for power), are derived from these basic units.
It’s important to use the correct units when measuring physical quantities, as this allows us to accurately compare and combine measurements from different sources. Additionally, using consistent units makes it easier to understand and interpret scientific results and data.
Who Decides the Units?
The decision on which units to use is made by international organizations and scientific communities. For example, the International System of Units (SI) is defined and maintained by the International Bureau of Weights and Measures.
Physical Quantities
Physical quantities are measurable properties of matter or energy. They can be described in terms of size, amount, or degree. Some examples of physical quantities include:
- Length: the size of an object, such as its height, width, or depth
- Mass: a measure of the amount of matter in an object
- Time: a measure of the duration of an event
- Temperature: a measure of the thermal energy of an object
- Speed: a measure of how fast an object is moving
- Force: a measure of the interaction between two objects that causes a change in motion
- Energy: a measure of the ability to do work
- Power: a measure of the rate at which energy is being used or converted
- Electric charge: a measure of the amount of electric charge in an object
- Electric current: a measure of the flow of electric charge
Fundamental and Derived Physical Quantities
Fundamental physical quantities are basic, independent physical measurements that are used as a basis for all other physical measurements. These quantities are used to define the units of measurement and cannot be expressed in terms of other quantities. Examples of fundamental physical quantities include length, mass, time, electric current, temperature, and amount of substance.
Derived physical quantities are physical measurements that are defined in terms of one or more fundamental physical quantities. These quantities are not independent and can be expressed in terms of the fundamental quantities.
In short, fundamental physical quantities are the building blocks of all other physical measurements, while derived physical quantities are built on top of these building blocks.
What is the SI system of Units?
The SI system of units, also known as the International System of Units, is the most widely used system of units for scientific measurement. The SI system was established by the International System of Units (SI) in 1960 and is based on seven base units for seven base quantities that are required to describe the physical world around us. These base units are:
- Meter (m) for length
- Kilogram ( kg) for mass
- Second ( s) for time
- Ampere ( A) for electric current
- Kelvin ( K) for temperature
- Mole ( mol) for amount of substance
- Candela ( cd) for luminous intensity
The SI system is an organized system of units that allows for consistent, accurate, and reproducible measurements. The system is widely used in scientific and engineering applications and is constantly being updated and refined to keep pace with advances in measurement technology.
Examples of some derived physical quantities:
- Velocity: SI Unit of velocity is \rm m/s because velocity = displacement/time (displacement is measured in meters and time is measured in seconds).
- Acceleration: Since acceleration = velocity/time the SI unit of acceleration is \rm m/s^2.
- Force: Force = mass \times acceleration so its SI unit is \rm kg.m/s^2 which is also called Newton.
- Energy: Energy = Force \times displacement so its unit is \rm Nm which is also called Joule.
- Power: Power = W/t so its SI unit will be \rm Nm/s which is specially called Watt.
- Pressure: Pressure = F/A so its SI unit is \rm N/m^2 .
Numerical questions:
Question No. 1
The SI and CGS units of energy are joule and erg respectively. How many ergs are equal to one joule?
Solution:
\begin{aligned}1\ \text{Joule} &= 1\ \rm Nm\\ &= 1\ \rm kgm^2/s^2\\\end{aligned}
As you know in the CGS unit, length is measured in \rm cm, mass is measured in grams and time in seconds. So, let’s change \rm kg in \rm gram and \rm meter in \rm cm .
\begin{aligned}1\ \rm Joule &= 1\ \rm Nm\\ &= 1 \rm kgm^2/s^2\\&= 1000\times10^2 \rm gcm^2/s^2\\&= 10^5 \rm ergs \\\end{aligned}
Therefore, 1 \rm Joule = 10^5 \rm ergs.
Question No. 2
Marie drives 10.0 \rm km from her college to home in 10.0 \rm min. Calculate Marie’s average speed (a) in kilometers per hour ( \rm km/h) and (b) in meters per second (\rm m/s).
Solution:
Here first we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correct conversion factor and multiplying by it.
The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in its place.
Solution for part (a)
Average speed is the total distance traveled divided by time of travel.
\begin{aligned}\text{average speed} &= \dfrac{\text{distance}}{\text{time}}\\ &= \dfrac{10.0\ \rm km}{20.0\ \rm min}\\ &= 0.500\ \rm km/min\\\end{aligned}
Now we want to convert \rm km/min to \rm km/h. For this, we need to multiply it by the conversion factor that will cancel minutes and leave hours.
Since 1\ \rm hr = 60\ \rm minutes so the conversion factor is 60\ \rm min/hr . Thus,
\begin{aligned}\text{average speed} &= 0.500\ \rm km/min \times 60\rm min/h\\ &= 30.0\ \rm km/h\\\end{aligned}
Solution for part (b)
We have
\text{average speed} = 0.500\ \rm km/min
In this part, we want to convert \rm km/min to \rm m/s. For this, we need to multiply it by a suitable conversion factor.
Since 1\ \rm km = 1000\ \rm m and 1\ \rm min = 60\ \rm sec so,
\begin{aligned}\text{average speed} &= 0.500\ \rm km/min \times 1000\ \rm m/1\ \rm km \times 1\ \rm min/60\ \rm s\\ &= 8.33\ \rm m/s\\\end{aligned}