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Physics / Mechanics

Newton's Laws of Motion

Newton's laws of motion state the relationship between the forces acting on an object and the resulting movement of the object. There are three laws proposed by Isaac Newton with regards to the motion of the object, popularly known as Newton's first law, second law and third law of motion.

Three Laws of Motion

Newton's three laws of motion are given below,

  • Newton's First Law of Motion: Every body tries to continue in its own state of rest or of uniform motion as long as no net external force acts on it. The body remains at its original state because of Inertia. Inertia is of 3 types, Inertia of Rest, Inertia of Motion and Inertia of Direction (a special case of Inertia of Motion). Mass is responsible for inertia of the body. Force is an external agent, which tries to change the state of the body.

  • Newton's Second Law of Motion: It states that the time rate of change of momentum (p) of an object is directly proportional to the applied force, and the change in momentum happens in the direction of the force applied.

    Time rate of change of momentum, F = dp/dt = ( pf – pi )/( tf – ti )

    Since p = mv, F = m ( vf – vi )/( tf – ti )

    Therefore, F = ma

  • Newton's Third Law of Motion: To every action, there is an equal and opposite reaction, from which it can be inferred that in nature, the forces always appear in pairs.

Law of Conservation of Momentum

    For a given system in a given process, the total momentum of the system remains constant. According to this law, the total momentum of the entire system after the process is equal to the total momentum of the system before the process.

    For example, before firing a bullet from a gun, the total momentum of the system is zero.

    After the bullet is fired from the gun,

    The total momentum of the gun and bullet system = mbvb + mgvg, where 'b' represents bullet and 'g' represents gun

    But according to Newton's Third Law, Fb = -Fg

    Therefore, dpb/dt = -dpg/dt

    As the time is constant, dpb = -dpg

    mbvb - 0 = - ( mgvg - 0 )

    mbvb+mgvg = 0

    So, the total momentum of the system remains constant before and after firing a bullet from a gun.

Relative Velocity

  • The velocity of a body which is measured with respect to another body, which is also in motion, is called relative velocity between them.
    v12 = v2 - v1

  • When two bodies are moving in the same direction then the relative velocity between them is given by the difference of their velocities and when two bodies are moving opposite to each other then the relative velocity is given by sum of their velocities.