Newtons laws of motion

Newton’s Laws of Motion Inertia The inherent property of objects to remain at rest unless it is acted upon by an external force is called inertia. In the case of bodies in uniform motion they can not change that state of motion by themselves in the absence of external forces. It is also called inertia of the body. First law of motion Every body continues in its state of rest or state of uniform motion along a straight line unless it is compelled by an external force to change that state. First enables us to define force. Force is that which changes or tends to change the state of rest or state of uniform motion of a body along a straight line. Momentum The property of a body by virtue of which it imparts or tends to impart motion to another body is called its momentum. Let a body of mass m be moving with velocity v. Its momentum p is given by P = m v It is a vector quantity Its unit is kg m/s. Second Law of Motion The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force is acting. Consider a body of mass m moving with velocity u. Let a constant force F act on the body for a time t seconds. Let the velocity of the body change From u to v. Initial momentum of the body = mu Final momentum of the body = mv Change in momentum produced = mv – mu Or rate of change momentum produced = mv – mu = m(v – u) = ma Where a is the acceleration produced t t According to Newton’s second law rate of change of momentum is directly proportional to the applied force. Hence we have ma ∞ F Or F ∞ ma F = kma Where k is a costant The constant k can be made equal to one by suitably defining the unit of force. When F = 1 m = 1 a = 1 then k = 1 Hence we get F =ma Unit force is the Newton. One Newton is that force which when acting on a body of unit mass produces in it an acceleration of one unit. Law of conservation of momentum In the absence of external forces when bodies exert force on each other the total momentum of the system of bodies will be conserved. In the case of collision of two bodies the total momentum before and after Collision will remain constant Third law To every action there is an equal and opposite reaction. Or action and reaction are equal and opposite Recoil of gun, Rocket propulsion are some examples in which we find the application of third law. Impulse and momentum Impulse = change in momentum produced I = mv-mu