Physical Quantities and units

⇒ 1. Physical Quantities:

• A physical quantity is a measurable attribute of an object or system that can be expressed numerically. Physical quantities are used to describe the physical properties of a system, such as its motion, energy, temperature, and more.
• Physical quantities are divided into base quantities and derived quantities.
• Base Quantities:
• – Base quantities are the fundamental physical quantities that cannot be expressed in terms of other physical quantities. They are the building blocks of physical quantities.
• Derived Quantities:
• – Derived quantities are physical quantities that can be expressed in terms of base quantities. They are derived from the base quantities through various mathematical operations like multiplication, division, and exponentiation.

2. S.I Units:

• I. units, also known as International System of Units, are the standard units of measurement used in physics and other sciences. The S.I. system consists of seven base units and several derived units.
• ⇒ Base unit:
• These are the fundamental units that cannot be expressed in terms of other units. They are the building blocks of the S.I. system. There are 7 base units.

Table 1 Base quantities and base units

• ⇒ Drive units:
• These are units that can be expressed in terms of the base units. They are derived from the base units through various mathematical operations like multiplication, division, and exponentiation.

Table 2 Drive quantities and drive units

• ⇒ Unit prefixes:
• Unit prefixes are used to modify the base units to express larger or smaller quantities.
• There is huge variation in the size of things.
• For example, the diameter of the Universe is about [math] 10^{24} [/math] m, and the diameter of an atomic nucleus about [math] 10^{−15} [/math]
• We often use standard form to help us write down very big and very small numbers in a quick and efficient way, rather than typing very long numbers with lots of digits into calculators or writing them out in full when performing written calculations.
• We can also use prefixes to show the size of a quantity in comparison to the S.I. unit at a power of ten expressed in standard form.

Table 3 Some common prefixes

• ⇒ Examples:
• (1)
• Divide 20,000 g by 1000 to express it into kilogramme, since kilo represents or [math]10^3 \text{ or } 1000[/math].
• [math]20,000g = \frac{20,000}{1000} kg = 20kg [/math]
• Or
• [math]20,000g = 20 × 10^3 g = 20kg [/math]
• Let us consider few more examples:
• (2)
• [math]200,000ms^{-1} = 200 × 10^3 ms^{-1} = 200kms^{-1} [/math]
• (3)
• [math]4,800,000 W = 4800 × 10^3 W = 4800 kW \\ 4,800,000 W = 4.8 × 10^6 W = 4.8MW[/math]
• (4)
• [math]\begin{gather} 0.000,000,0081 m = 0.0081 × 10^{-6} m = 8.1 × 10^{-9} m \\ 8.1 × 10^{-9} m = 8.1nm \end{gather}[/math]
• ⇒ The homogeneity of equations:
• Use some equations for homogeneity
• (1)
• Equation of motion:
• [math]v=u+at[/math]
• – v is initial velocity and its S.I unit is [math]ms^{-1}[/math]
• – u is final velocity and its S.I unit is [math]ms^{-1}[/math]
• – a is acceleration and its S.I unit is [math]ms^{-2}[/math]
• – t is time and its S.I unit is
• – Use all these S.I units in equation
• [math] \begin{gather} v = u + at \\
  \text{ms}^{-1} = \text{ms}^{-1} + (\text{ms}^{-2})(s) \\
  \text{ms}^{-1} = \text{ms}^{-1} + \text{ms}^{-1} \end{gather}[/math]
• – So, the same units add with each other
• (2) 
• Equation of momentum:
• [math]p = mv[/math]
• – p is momentum and its S.I unit is [math]\text{kg}\,\text{ms}^{-1} [/math]
• – m is mass of any particular body and its S.I unit is  [math]\text{kg} [/math]
• – v is velocity of that body and its S.I unit is [math]ms^{-2}[/math]
• – So, use these S.I units in equation
• [math]\begin{gather} p = mv \\ \text{kg} \,\text{ms}^{-1} = (\text{kg})(\text{ms}^{-1}) \\ \text{kg} \, \text{ms}^{-1} = \text{kg} \,\text{ms}^{-1} \end{gather}[/math]
• (3)
• 2^nd Newton’s Law:
• [math] F = ma [/math]
• – F is force and its S.I unit is N (newton) or [math]\text{kg}\,\text{ms}^{-2} [/math]
• – M is mass of a body and its S.I unit is [math]\text{kg} [/math]
• – a is acceleration and its S.I unit is [math]ms^{-2}[/math]
• So, the equation becomes
• [math]\begin{gather} F = ma \\ \text{kg}\,\text{ms}^{-2} = (\text{kg})(\text{ms}^{-2}) \\
  \text{kg}\,\text{ms}^{-2} = \text{kg}\,\text{ms}^{-2} \end{gather}[/math]
• (4)
• Equation for measurement of pressure:
• [math] p = \frac{F}{A}[/math]
• – Pressure is represented by p and its S.I unit is [math]\text{N}\,\text{m}^{-2} \quad \text{or} \quad \text{kg}\,\text{m}^{-1}\,\text{s}^{-2} [/math]
• – F is force and its S.I unit is N (newton) or [math]\text{kg}\,\text{ms}^{-2} [/math]
• – A is cross sectional area and its S.I unit is [math]\text{ms}^{2} [/math]
• – So, equation becomes
• [math] \begin{gather} p = \frac{F}{A} \\ \text{kg}\,\text{m}^{-1}\,\text{s}^{-2} = \frac{\text{kg}\,\text{ms}^{-2}}{\text{m}^2} \\
  \text{kg}\,\text{m}^{-1}\,\text{s}^{-2} = \text{kg}\,\text{ms}^{-2}\,\text{m}^{-2} \\
  \text{kg}\,\text{m}^{-1}\,\text{s}^{-2} = \text{kg}\,\text{m}^{-1}\,\text{s}^{-2} \end{gather}[/math]