Applications of Vectors in Geometry

Vectors are such a powerful tool in mathematics and physics, that many results can be proved very easily and intuitively.     Statement : If the diagonals of a parallelogram are congruent, then it is a rectangle. Proof : Let $latex ABCD$ be the parallelogram. Let $latex A$ be the origin. So, the position vectors… Continue reading Applications of Vectors in Geometry

Curvilinear Motion

Introduction Curvilinear stands for along a curve. This is the most general specification of motion. It can either be two-dimensional or three-dimensional. Examples of 2D motions are motion of a projectile and circular motion. These involve motions along planar curves. Examples of 3D motions are a roller coaster, satellite launching etc. They follow a space… Continue reading Curvilinear Motion

Laws of Friction, Application in Pulleys, Brakes and Wedges

The Origin of Friction Friction is defined as the resistive force to motion, offered by the contacting surfaces. Another common observation is generation of heat from the contacting surfaces. The applied kinetic energy is converted to heat. The work done is $latex 0$, till the friction is overcome. The origin of friction is in the… Continue reading Laws of Friction, Application in Pulleys, Brakes and Wedges

Statics : Trusses, Cables and Frames

The analysis of trusses, cables and frames is based on the static equilibrium of these structures. So, the equations of equilibrium are extensively used. There are certain differences as far as the definitions are concerned, but the analysis is similar. Trusses  Structure of Howrah Bridge The Howrah bridge is a cantilever truss bridge, built in… Continue reading Statics : Trusses, Cables and Frames