Dynamics and Kinematics

Newton’s laws of motion 1st law – every body continues in a state of rest or uniform velocity unless compelled to do otherwise by an applied resultant force 2nd law – the rate of change of momentum brought about by an applied resultant force is directly proportional to the force and the change in momentum occurs in the direction of the force If a body A exerts a force on a body B, body B exerts an equal and opposite force on body A

Newton’s second law of motion Momentum, P is defined as the product of its mass (m) and its speed/velocity (v) P = m x v It is a vector quantity whose direction is the same as its velocity Unit: kgm/s or NS If a resultant force is applied to mass (m) for a time (t) then Initial momentum, Pi = mu and Pf = mv Change in momentum, ΔP = Pi - Pf = mv-mu

Laws Law of conservation of linear momentum states that the sum of the momentum of the interacting bodies in a given direction before interaction is equal to the sum of the momentum of the interacting bodies after the interaction in the same direction given that no external forces act on the bodies The law of conservation of total energy states that energy can neither be created nor destroyed but can be changed from one form to another

Collisions When bodies undergo interactions the laws of conservation if (linear) momentum and total energy are obeyed ( for elastic collisions though kinetic energy is conserved also) Collisions are either elastic or inelastic Elastic collisions are those collisions in which the sum of the kinetic energies of the colliding bodies before the collision is equal to the sum of the kinetic energies of the colliding bodies after the collision Inelastic collisions are those in which the sum of the kinetic energies of the colliding bodies before the collision is NOT equal to the sum of the kinetic energies of the colliding bodies after the collision A total inelastic collision is one in which the colliding bodies stick together during impact and move as one body with a common velocity,v after the collision