Mathematics

Statics and Dynamics

Statics
Composition & Resolution Of Two forces
Force
  • Resultant of Forces
  • Magnitude and Direction of the Resultant
Parallelogram Laws Of Forces
  • When p & q are at Right angle
  • When p & q inclined at an Angle Ù
  • When p & q are in the Same direction
  • When p & q are in the Opposite direction
Components & Resolved Parts Of A force
  • The Component of F
  • Resolved parts of the Force
Coplanar Forces Acting At A Point
Resultant Of A number Of Coplanar Forces Acting At A Point
  • Proving properties to find the Resultant
  • Magnitude & Direction of the Resultant
Condition Of Equilibrium Of A Number Of Coplanar Forces
  • Magnitude & Direction of the Fourth Force
  • To Prove the Forces are in Equilibrium
Equilibrium Of Three Concurrent Forces
Problems involving Laws & Theorems
  • Triangle Law of forces
  • Converse of Triangle Law of Forces
  • Polygon of Forces
  • Lami's Theorem
  • â-µ Theorem
  • Ratio of three Forces
Tension In The string
  • To find the Tension
  • Prove for the Tension
Parallel Forces
Like & Unlike Forces
  • Direction, Magnitude & Position
  • Find the Larger force
  • Equilibrium of a Rod Supported on two Pegs
Resultant
  • If the Forces are Like & Parallel
  • If the Forces are Unlike & Parallel
  • To Find the Ratio of distances of the Resultant
Moment Of A Force
  • Varignon's Theorem
  • Generalization of Varignon's Theorem
Couples
  • Composition of Coplanar Couples
  • Triangle Theorem
  • Polygon Theorem
  • Resultant of a Force & a Couple
Dynamics
Motion In A Straight Line
Velocity & Acceleration Of A Moving Point
  • Expression for Velocity
  • Expression for Acceleration
Motion In A Straight Line With Uniform Acceleration
  • Equation of motion
  • Distance traversed in nth second
  • Distance traversed in t seconds
Motion Under Gravity
  • Bodies falling freely
  • Bodies projected vertically upwards
  • Maximum Height
  • Time of Flight
Newton's Laws Of Motion
Laws Of Motion
  • First Law of Motion
  • Second Law of Motion
  • Third Law of Motion
Motion Of A Lift
  • Motion of a Lift moving Upwards
  • Motion of a Lift moving Downwards
  • Effective Force stopping a falling body
  • Resistance of sand on a Body falling in sand
Composition & Resolution Of Velocity
Resultant & Components Of Velocities
  • Parallelogram of velocities
  • Resultant of two velocities when u & v are at right angle
  • Resultant of two velocities when u & v are equal
  • The Triangle of velocities
Resolution Of Velocities In Given Direction
  • When Ù + Ú = Æ/2
  • Sum of resolved parts of two velocities
Composition Of A Number Of Velocities
  • Polygon of velocities
  • Composition of velocities by resolving along Two Axes
Relative Velocity
  • When a & b are moving in the Same Direction
  • When a & b are moving in Opposite Direction
  • When a & b are inclined at an Angle Ø
Projectile
Motion Of A Projectile And Its Trajectory
  • Latus Rectum, Vertex, Focus, Directrix of Trajectory
  • Time of Flight of the Projectile
  • Range of Flight of the Projectile
  • Maximum Range of the Projectile
  • Greatest Height attained by the Projectile
  • Time Taken by the Projectile to reach the Greatest Height
Velocity Of The Projectile
  • Velocity at any point
  • Velocity at a given Height of the Projectile
  • Locus of the Focus of the Trajectory of a Projectile
  • Locus of the Vertex of the Trajectory of a Projectile