AS Physics Physical quantities Study Notes
AS Physics Physical quantities Study Notes
AS Physics Physical quantities Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on AS Physics Study Notes syllabus with guiding questions of
- understand that all physical quantities consist of a numerical magnitude and a unit
- make reasonable estimates of physical quantities included within the syllabus
Standard level and higher level: 3 hours
Additional higher level: 1 hour
Understanding Physical Quantities
A physical quantity is any property of a material or system that can be measured and expressed as a number multiplied by a unit.
Every physical quantity therefore has two essential components:
- Numerical magnitude: the number that tells “how much” of the quantity is present.
- Unit: the defined standard used for comparison or measurement.
For example, when we say an object’s length is \( \mathrm{5\,m} \):
- The number 5 is the magnitude.
- The symbol m (metre) represents the unit.
Key Idea: The value of a physical quantity is only meaningful when both its numerical magnitude and unit are stated together.
Representation:
The general relationship between a physical quantity, its magnitude, and its unit is written as:
\( \mathrm{Q = n \times u} \)
- \( \mathrm{Q} \): physical quantity
- \( \mathrm{n} \): numerical magnitude (number)
- \( \mathrm{u} \): unit
Common Physical Quantities:
| Physical Quantity | Symbol | SI Unit | Unit Symbol |
|---|---|---|---|
| Length / Distance | \( \mathrm{l,\,x,\,r} \) | metre | \( \mathrm{m} \) |
| Mass | \( \mathrm{m} \) | kilogram | \( \mathrm{kg} \) |
| Time | \( \mathrm{t} \) | second | \( \mathrm{s} \) |
| Electric current | \( \mathrm{I} \) | ampere | \( \mathrm{A} \) |
| Temperature (thermodynamic) | \( \mathrm{T} \) | kelvin | \( \mathrm{K} \) |
| Amount of substance | \( \mathrm{n} \) | mole | \( \mathrm{mol} \) |
| Luminous intensity | \( \mathrm{I_v} \) | candela | \( \mathrm{cd} \) |
| Area | \( \mathrm{A} \) | square metre | \( \mathrm{m^2} \) |
| Volume | \( \mathrm{V} \) | cubic metre | \( \mathrm{m^3} \) |
| Velocity / Speed | \( \mathrm{v,\,u} \) | metre per second | \( \mathrm{m/s} \) |
| Acceleration | \( \mathrm{a} \) | metre per second squared | \( \mathrm{m/s^2} \) |
| Force | \( \mathrm{F} \) | newton | \( \mathrm{N} = \mathrm{kg\,m/s^2} \) |
| Pressure | \( \mathrm{p} \) | pascal | \( \mathrm{Pa} = \mathrm{N/m^2} \) |
| Energy / Work / Heat | \( \mathrm{E,\,W,\,Q} \) | joule | \( \mathrm{J} = \mathrm{N\,m} \) |
| Power | \( \mathrm{P} \) | watt | \( \mathrm{W} = \mathrm{J/s} \) |
| Charge | \( \mathrm{Q} \) | coulomb | \( \mathrm{C} = \mathrm{A\,s} \) |
| Potential difference (Voltage) | \( \mathrm{V} \) | volt | \( \mathrm{V} = \mathrm{J/C} \) |
| Resistance | \( \mathrm{R} \) | ohm | \( \mathrm{\Omega = V/A} \) |
| Capacitance | \( \mathrm{C} \) | farad | \( \mathrm{F = C/V} \) |
| Magnetic flux | \( \mathrm{\Phi} \) | weber | \( \mathrm{Wb} \) |
| Magnetic flux density | \( \mathrm{B} \) | tesla | \( \mathrm{T = Wb/m^2} \) |
| Frequency | \( \mathrm{f} \) | hertz | \( \mathrm{Hz = s^{-1}} \) |
| Angular velocity | \( \mathrm{\omega} \) | radian per second | \( \mathrm{rad/s} \) |
| Angular acceleration | \( \mathrm{\alpha} \) | radian per second squared | \( \mathrm{rad/s^2} \) |
| Momentum | \( \mathrm{p} \) | kilogram metre per second | \( \mathrm{kg\,m/s} \) |
| Impulse | \( \mathrm{I} \) | newton second | \( \mathrm{N\,s} \) |
| Density | \( \mathrm{\rho} \) | kilogram per cubic metre | \( \mathrm{kg/m^3} \) |
| Specific heat capacity | \( \mathrm{c} \) | joule per kilogram per kelvin | \( \mathrm{J/(kg\,K)} \) |
| Specific latent heat | \( \mathrm{L} \) | joule per kilogram | \( \mathrm{J/kg} \) |
| Spring constant | \( \mathrm{k} \) | newton per metre | \( \mathrm{N/m} \) |
| Torque / Moment of force | \( \mathrm{\tau} \) | newton metre | \( \mathrm{N\,m} \) |
| Work function (photoelectric effect) | \( \mathrm{\phi} \) | joule | \( \mathrm{J} \) |
| Wavelength | \( \mathrm{\lambda} \) | metre | \( \mathrm{m} \) |
| Refractive index | \( \mathrm{n} \) | dimensionless | — |
| Efficiency | \( \mathrm{\eta} \) | dimensionless (ratio) | — |
Example
A car travels a distance of \( \mathrm{120\,km} \) in \( \mathrm{2\,hours} \). Find its speed and express it as a physical quantity in standard SI units.
▶️ Answer / Explanation
Step 1: Write the formula for speed.
\( \mathrm{v = \dfrac{d}{t}} \)
Step 2: Convert all quantities to SI units.
\( \mathrm{d = 120\,km = 1.20\times10^5\,m} \)
\( \mathrm{t = 2\,h = 7200\,s} \)
Step 3: Calculate the speed.
\( \mathrm{v = \dfrac{1.20\times10^5}{7200} = 16.7\,m/s} \)
Step 4: State as a physical quantity.
\( \mathrm{v = 16.7\,m/s} \)
Interpretation: The numerical magnitude is 16.7 and the unit is m/s (metre per second).
Making Reasonable Estimates of Physical Quantities
In physics, an estimate is an approximate value of a quantity, based on reasoning, experience, or simplified calculation, rather than precise measurement.
Estimating helps physicists and engineers judge whether an answer or measurement is physically realistic and within the expected range of values.
Purpose of Estimation:
- To check whether calculated results are reasonable.
- To plan experiments or predict outcomes when exact data are unavailable.
- To develop physical intuition about the scales and magnitudes of real-world quantities.
Approach to Making Estimates:
- Use order of magnitude reasoning (e.g., powers of 10).
- Use typical known values — e.g., mass of a person ≈ 70 kg, speed of sound ≈ 340 m/s.
- Make simplifying assumptions (ignore small effects or use rounded values).
- Perform quick, approximate calculations to get a plausible result.
Key Idea: Estimation allows you to evaluate the realism of a result before or after detailed calculation — a crucial skill in experimental and applied physics.
Common Examples of Reasonable Estimates:
| Physical Quantity | Typical Value (Order of Magnitude) | Example Context |
|---|---|---|
| Diameter of an atom | ≈ \( \mathrm{10^{-10}\,m} \) | Typical atomic scale |
| Wavelength of UV light | ≈ \( \mathrm{10\,nm = 1\times10^{-8}\,m} \) | Ultraviolet region of EM spectrum |
| Height of an adult human | ≈ \( \mathrm{2\,m} \) | Average person |
| Distance between Earth and Sun (1 AU) | ≈ \( \mathrm{1.5\times10^8\,m} \) | Average Earth–Sun distance |
| Mass of a hydrogen atom | ≈ \( \mathrm{10^{-27}\,kg} \) | Smallest atom mass |
| Mass of an adult human | ≈ \( \mathrm{70\,kg} \) | Average adult body mass |
| Mass of a car | ≈ \( \mathrm{1000\,kg} \) | Standard family car |
| Seconds in a day | ≈ \( \mathrm{9.0\times10^4\,s} \) | 24 hours = 86,400 s |
| Seconds in a year | ≈ \( \mathrm{3\times10^7\,s} \) | 365 days × 24 h × 3600 s |
| Speed of sound in air | ≈ \( \mathrm{3\times10^2\,m/s} \) | At 20 °C in air |
| Power of a light bulb | ≈ \( \mathrm{60\,W} \) | Typical household bulb |
| Atmospheric pressure | ≈ \( \mathrm{1\times10^5\,Pa} \) | Standard atmospheric pressure at sea level |
| Length of a car | ≈ \( \mathrm{4\,m} \) | Average family vehicle |
| Acceleration due to gravity | ≈ \( \mathrm{9.8\,m/s^2} \) | Near Earth’s surface |
| Mass of an electron | ≈ \( \mathrm{9\times10^{-31}\,kg} \) | Subatomic particle |
| Radius of Earth | ≈ \( \mathrm{6.4\times10^6\,m} \) | Mean radius |
Example
Estimate the time it takes for sound to travel from a lightning strike 1 km away to reach an observer.
▶️ Answer / Explanation
Step 1: Use the formula \( \mathrm{t = \dfrac{d}{v}} \).
Given: \( \mathrm{d = 1.0 \times 10^3\,m} \), \( \mathrm{v = 3.4 \times 10^2\,m/s} \).
Step 2: Estimate the time:
\( \mathrm{t = \dfrac{1.0 \times 10^3}{3.4 \times 10^2} \approx 3\,s.} \)
Interpretation: The sound will reach the observer about 3 seconds after the lightning is seen — a reasonable estimate matching real-world experience.