PHY 101 VOL_1

1. Units and Measurements

  • Physics is the study of all aspects of the universe, requiring careful and accurate measurements.

  • Fundamental dimensions: length, mass, and time.

  • Units must be defined; SI units are now universally accepted.

    • Length: meter (m)

    • Time: second (s)

    • Mass: kilogram (kg)

  • Physical quantities divided into fundamental and derived quantities.

  • Fundamental units list includes:

    • Length: meter (m)

    • Mass: kilogram (kg)

    • Time: second (s)

    • Temperature: kelvin (K)

    • Current: ampere (A)

    • Amount of substance: mole (mol)

    • Luminous intensity: candela (cd)

1.1 Time

  • Definition of the second based on atomic clock; 9192631770 cycles of cesium atom's microwave radiation.

  • Time interval is the difference between times of two events, measured using:

    • Clocks and watches for minutes or hours.

    • Stop clocks for seconds.

    • Fractions of a second: nanoseconds (ns), microseconds (µs), milliseconds (ms).

1.2 Length

  • Current definition of meter: distance light travels in vacuum in 1/299792458 seconds.

  • Length measurement units include:

    • Nanometer (nm): 10^-9 m

    • Micrometer (µm): 10^-6 m

    • Millimeter (mm): 10^-3 m

    • Centimeter (cm): 10^-2 m

    • Kilometer (km): 10^3 m

  • Instruments for length measurement:

    • Metre rule

    • Tape measure

    • Vernier calipers (accurate to 1/10 mm)

    • Micrometer screw gauge (accurate to 1/100 mm)

1.3 Mass

  • Mass is the quantity of matter in an object, unit is kilogram (kg).

  • Weight is a force; gravitational pull on an object measured in newtons (N).

  • Mass remains constant, weight varies with position.

  • Measurement tools: chemical balance, lever balance, spring balance.

    • Sub-multiples include:

      • Microgram (µg): 10^-6 g = 10^-9 kg

      • Milligram (mg): 10^-3 kg

      • Gram (g): 10^-3 kg

1.4 Measurement of Volume

  • Graduated cylinder used for liquid volume measurement, accurate to nearest 1cm³.

  • Displacement method for irregularly shaped objects.

1.5 Dimensional Analysis

  • Dimensions relate physical quantities to fundamental quantities (length L, mass M, time T).

  • Every equation must maintain dimensional consistency.

  • Example: For distance = speed × time:

    • Distance (L) = (L/T) × T (T cancels out)

    • Illustration of dimensional consistency in physics.

2 Vectors

  • Scalar quantities: magnitude only; examples: length, time, mass.

  • Vector quantities: magnitude and direction; examples: displacement, velocity.

  • Vectors represented by arrows where length represents magnitude.

2.1 Addition of Vectors

  • Vectors added using the parallelogram method; diagonal represents the resultant vector.

  • Resolving vectors into components (Rx, Ry):

    • Rx = R cos θ

    • Ry = R sin θ

2.2 Relative Velocity

  • Velocity of one object relative to another – vector addition of velocities.

  • Example of velocity calculation for two vehicles moving in the same direction.

2.3 Unit Vectors

  • Unit vectors defined as having magnitude of one, expressed as ˆi, ˆj, ˆk for x, y, z axes respectively.

  • Vector R can be expressed in component format: R = Rx ˆi + Ry ˆj + Rz ˆk.

2.4 Vector Multiplication

  • Scalar (Dot) Product: A · B = AB cos φ.

    • Equals sum of components in vector format.

  • Vector (Cross) Product: A × B = AB sin φ with determinants.

3 Motion in One Dimension

  • Kinematics: study of motion without forces.

  • Displacement formula: ∆x = x2 - x1.

  • Average velocity: v = ∆x / ∆t.

  • Instantaneous velocity defined as: vi = lim ∆t→0 ∆x/∆t.

  • Acceleration measures change in velocity; examples given with calculations.

3.1 Motion with Constant Acceleration

  • Deriving equations of motion for constant acceleration.

    • Key equations for velocity and displacement derived.

3.2 Freely Falling Bodies

  • Objects under gravity experience same acceleration (g = 9.8 m/s²).

  • Various equations of motion derived for bodies in free fall.