Unit and Measurement 02 Class Notes PDF

# CDS/CAPF 2025 ## Physics - Lecture 02 ### Unit and Measurement - 2 By - Vikrant Pundir ### Topics to be covered 1. Unit & Measurement - राशियाँ 2. Distance, Displacement, Velocity, Acceleration 3. Dimensional Formula 4. Nomenclature (Units, Prefixes) ### Revision - Fundamental unit - Length...

# CDS/CAPF 2025 ## Physics - Lecture 02 ### Unit and Measurement - 2 By - Vikrant Pundir ### Topics to be covered 1. Unit & Measurement - राशियाँ 2. Distance, Displacement, Velocity, Acceleration 3. Dimensional Formula 4. Nomenclature (Units, Prefixes) ### Revision - Fundamental unit - Length - m - Mass - kg - Time - s - Temp - K - Amount of Substance - Mole - Luminous Intensity - Candela - Current - Ampere - Supplementary unit - Plane Angle - radian - Solid Angle - steradian ### Derived Unit - or more than 2 fundamental units. ### Examples - Speed - m/sec - 1 Newton = Force = m*a - a = m/sec² ### Sine Wave - sin(0) = 0 - sin(π/2) = 1 - sin(π) = 0 - sin(3π/2) = -1 - sin(2π) = 0 ### System Of Unit - LMT (CGS) - cm - gram - sec - FPS - foot - pound - sec - MKS - metre - kg - sec - SI - Similar to MKS, it's the standard system of unit. ### Quantity - Scalar Quantity - Only Magnitude (v) - But no Direction (x) - Examples - 5 cm, 50 gm, 50 sec - Examples - Distance, Mass, Time, Pressure, Strain, Speed - Vector Quantity - Which have Magnitude and Direction - Also follow the vector law of triangle addition - Examples - Velocity, Displacement, Acceleration, Force - Tensor Quantity - Which have Magnitude and Direction - But do not follow the vector law of triangle addition. - Examples - Current, Temperature ### Vector Quantity - Shown by using an arrow (->) - Examples - Velocity (v) - Acceleration (a) - Displacement (s) ### Magnitude - Shown by using 1x1 or modulus - Note: Any vector quantity has both magnitude and direction. - Vector = Magnitude * Direction ### Unit Vector - If |Magnitude| = 1 (|a| = 1) - Note: - Any vector - |Magnitude| = 1 - Direction (cap) ### Direction - Shown by using a cap - Examples - 3i + 4j = x - i, j, k represent x, y, z axis. ### Magnitude - √(3² + 4²) = √25 = 5 ### Vector Law Of Triangle Addition - Tail - Head - Point - Direction - Triangle - 3 sides - Rules - Only 3 Vectors - Combine all the 3 vectors in such a way that it will form a triangle. Remember that you can’t change their Direction. ### Examples - AB, BC, AC - AC = AB + BC (logic) - Resultant = Magnitude ### Rules to remember 1. Head & tail of the same vector should coincide. 2. Not coinciding ### Tensor Quantity - scalar - Current - I - I = 2 Amp - I = 5 Amp - Magnitude - Direction - +ve & - ve - Q - Charge - Electron - Law of Vector Addition (X) ### Current - Follows - KVL - Kirchoff’s Voltage Law - KCL - Kirchoff’s Current Law - junction law - Incoming current = outgoing current ### Examples - Lko, Delhi, Meerut, Punjab, Haryana. - Junction - Incoming current = I₁+ I₂ + I₃ - Outgoing current = I₄ + I₅ + I₆ - I₁ + I₂ + I₃ = I₄ + I₅ + I₆ - I_in = +ve - I_out = -ve ### Modulus - -2 -> Modulus -> Magnitude = |-2| = +2. - -y -> Modulus -> Magnitude = |-y| = +y. ### Usage of scalar, vector, tensor: - Distance - Scalar - Total path covered by an object = (8 + 1 + 1 + 1 + 1 + 1 +...)m = 7 m - Displacement - Vector - Shortest path between initial and final point = (8 + 1) m = 9 m = 5 cm - AC = AB + BC = √(AB² + BC²) = √(3² + 4²) = 5 m. ### Few points about Displacement - Distance = Displacement only & only in straight line path. - Initial point, Final point. - Distance = AB + BC = 100 + 50 = 150 m. - Displacement = 50 m. ### Examples - Start & stop = 50 m - Distance = AB + BA = 50 + 50 = 100 m. - Displacement = 0 m. - Round trip - 1 round - 2 round - 3 round - 9 round - Displacement = 0 ### Examples - Initial point (I.P) +y - Final point (F.P) - Displacement = 2 m - Could be -ve also A picture of the tank against a fiery apocalyptic background with "JAI HIND" written in bold below it.