Physical quantities

• Does direction of wind matter when you fly a kite?

  You need to know the direction in which the air is blowing; otherwise, it will be difficult for you to keep your kite flying
• Scalar quantities


  Physical quantities which can be completely described only by its numerical magnitude (or size) with proper unit
• Scalar quantities can be added, subtracted and multiplied by using ordinary rules of algebra
• Vector quantities


  Physical quantities which require not only numerical magnitude (or size) with proper unit, but also the direction
• To fully describe a vector, its direction must be specified
• Vector quantities cannot be added, subtracted, or multiplied using the usual rules of algebra
• Vector quantities follow their own set of rules known as vector algebra
• Coordinate system


  Used to locate the position of any point and that point can be plotted as an ordered pair (x, y) known as Coordinates
• 1. axis


  The horizontal number line
• 1. axis


  The vertical number line
• Origin


  The point of intersection of the X-axis and Y-axis, denoted as 'O'
• Reference frame


  The coordinate system from which the positions of objects are described
• Vector


  Symbolically represented by a letter, either capital or small, with an arrow over it
• Vector


  • Graphically represented by an arrow, the length of the arrow gives the magnitude with proper unit, and the arrow head points the direction of the vector
  • Placed in a coordinate axis to use
• Aeroplane route from Islamabad to Karachi


  • Shown as a vector in a geographical coordinate system having directions as North, East, West and South
• Steps to represent a vector in a coordinate system

  1. Choose and draw a coordinate system

  2. Select a suitable scale

  3. Draw a line in the fixed direction, cut the line equal to the magnitude of the vector according to the chosen scale

  4. Put an arrow along the direction of the vector
• Representation of helicopter motion

  • 20 km from origin towards 60° south of west
• Displacement, force, weight, velocity, acceleration, momentum, electric field strength, and gravitational field strength are vector quantities or vectors
• When combining two or more vectors, the resulting value must also result as a vector
• Vector addition


  1. Combining two or more vectors to into a single vector (called as resultant vector) to determine their cumulated effect

  2. Vectors can be added geometrically by drawing them to a common scale and placing them head to tail

  3. Joining the tail of the first vector with the head of the last will give another vector which will be its resultant vector
• Addition of three vectors


  • Shown in figure 1.5
• Addition of two vectors A and B

  • A is along x-axis, B is along y-axis, and they are perpendicular to each other
  • The resultant vector R is obtained by joining the tail of vector A with the head of vector B
• Prefix


  A mechanism through which numbers are expressed in power of ten that are given a proper name
• Prefixes make standard form or scientific notation further easier
• Large numbers are simply written in more convenient prefix with units
• Expressing measurements in smaller/larger units

  • Thickness of paper in millimetres instead of metres
  • Distance between cities in kilometres instead of metres
• Prefixes in SI to replace powers of 10

  • Yotta (10^24)
  • Zetta (10^21)
  • Exa (10^18)
  • Peta (10^15)
  • Tera (10^12)
  • Giga (10^9)
  • Mega (10^6)
  • Kilo (10^3)
  • Hecto (10^2)
  • Deca (10^1)
  • Deci (10^-1)
  • Centi (10^-2)
  • Milli (10^-3)
  • Micro (10^-6)
  • Nano (10^-9)
  • Pico (10^-12)
  • Femto (10^-15)
  • Atto (10^-18)
• Using prefixes


  • 86,400 seconds = 86.4 ks
  • Distance to Alpha Centauri = 41.32 Pm
  • Thickness of book page = 40 μm
  • Mass of grain of salt = 100 mg
• Volume is a derived quantity
• Derived units for International System of Units (SI)

  • Area (m^2)
  • Volume (m^3)
  • Speed/Velocity (m/s)
  • Acceleration (m/s^2)
  • Density (kg/m^3)
  • Force (N)
  • Pressure (Pa)
  • Energy (J)
• Standard form/Scientific notation


  Represents a number as the product of a number greater than 1 and less than 10 (mantissa) and a power of 10 (exponent)
• Using scientific notation


  • Width of observable universe = 8.8 x 10^26 m
  • Mass of Earth = 5.98 x 10^24 kg
  • Diameter of hydrogen nucleus = 1.7 x 10^-17 m
• SI base units


  • Length (m)
  • Mass (kg)
  • Time (s)
  • Electric current (A)
  • Temperature (K)
  • Amount of substance (mol)
  • Light intensity (cd)
• Measurements are not confined to science. They are part of our lives. They play an important role to describe and understand the physical world. Over the centuries, man has improved the methods of measurements.
• In this unit, we will study some of physical quantities and a few useful measuring instruments. We will also learn the measuring techniques that enable us to measure various quantities accurately.
• Physics


  The most fundamental of all the sciences. It is the study of matter, energy and their interaction.
• Physics is the most fundamental of all the sciences. In order to study biology, chemistry, or any other natural science, one should have a firm understanding of the principles of physics.
• Technologies based on physics principles

  • Computers
  • Smart phones
  • MP3 players
  • Internet
  • Rockets and space shuttles
  • Magnetically levitating trains
  • Microscopic robots that fight cancer cells
• Physics is behind every technology and plays a key role in further development of these technologies, such as airplanes, computers, PET scans and nuclear weapons.
• Physical quantities


  Quantities which can be measured