Scalar & Vector Notes.pdf

SCALAR & VECTOR QUANTITIES MECHANICS - Mechanics is the branch of physics concerned with the behaviour of physical bodies when subjected to FORCES and the subsequent effect of the bodies on their environment ∙ Statics - Forces, weight, moments, Hooke’s law ∙ Kinematics - Motion (v...

SCALAR & VECTOR QUANTITIES MECHANICS - Mechanics is the branch of physics concerned with the behaviour of physical bodies when subjected to FORCES and the subsequent effect of the bodies on their environment ∙ Statics - Forces, weight, moments, Hooke’s law ∙ Kinematics - Motion (velocity, acceleration, displacement, projectile) ∙ Dynamics - Laws of motion (Aristotle, Galileo, Newton), momentum ∙ Energy - Forms of energy, sources of energy, law of conservation of energy, power, efficiency, machines ∙ Hydrostatics - Pressure, Archimedes’ principle SCALAR & VECCTOR QUANTITIES A scalar quantity is one which has magnitude (size) only. A vector quantity is one which has magnitude (size) and direction. Let us consider the 7 basic quantities Length Mass Time Temperature Electric current Amount of substance Luminous intensity All are scalar!! Derived Quantity – How to tell if they are scalar or vector? There are two ways to determine whether a derived quantity is scalar or vector: Consider the definition of the quantity. Consider the formula used to obtain the quantity. Definition of the quantity Displacement is defined as distance moved in a given direction. From this definition we can conclude that displacement is a vector. The formula used to obtain the quantity. Example 1 Density depends on both mass and volume. Since both mass and volume are scalar quantities, then density is a scalar quantity. To determine whether a derived quantity is scalar or vector using a formula. PRODUCT OF QUANTITIES QUOTIENT OF QUANTITIES Scalar x Scalar = Scalar Scalar/Scalar = Scalar Scalar x Vector = Vector Scalar/Vector = Vector Vector/Scalar = Vector Vector x Vector = Scalar Vector/Vector = Scalar The formula used to obtain the quantity. Example 2 Speed is a scalar quantity because it is obtained when a Scalar/Scalar. Velocity is a vector quantity because it is obtained when a Vector/Scalar. Adding and subtraction scalars Combining (adding and subtraction vectors) Parallel vectors Vectors 90° acting from the same point Vectors acting from the same point at any angle other than 90° Parallel Vectors Vectors acting 90° to each other Vectors acting any angle to each other Resolving a vector Breaking a vector into components 12ms-1 ϴ = 45° 25N  Fr-frictional R-reaction force R F-force pulling ↑ w-weight. X fr G W  9 40