Newton's Laws of Motion, newton's second law ,Inertia and Mass

(3) Newton's First law of Motion

  • We have already stated Newton's First law of motion which says that a body would continue to be in state of rest or continue to move with constant velocity unless acted upon by a net external force
  • Here the net external force on the body is the vector sum of all the extenal forces acting on the body
  • When the body at rest or in a state of motion with uniform velocity then in both the cases acceleration is zero.This implies that
    a=0 for F=0

  • When net forces i.e vector sum of all the forces acting on the body is zero.the body is said to be in equilbrium .When rotational motion is involved <,net torque on body should also be zero i.e their is no change in either translational or rotational motion
  • Since forces can be combined according to the rules of vector addition.Thus for a body to be in equilibrium
    or in component form
    These are the condition for the body in translational equilibrium
  • We will discuss about rotational equilibrium while studying torque and rotational motion
  • Thus Newton's First law of motion quantitatively defines the concept of force as a influence that changes the state of motion of the body
  • It does not say anything about what has to be done to keep object moving that is once the body gains motion by the application of force would it always remains in the state of motion or it would come to rest
  • According to first law if we completely eliminates frictional forces, no forward force at all would be required to keep an object ( say a block on table) moving once it had been set in motion

(4) Inertia and Mass

  • From First law of motion an object at rest would not move unless it is acted upon by a force
  • This inherent property of objects to remain at rest unless acted upon by a force is called intertia rest
  • Now consider the case of an object moving with uniform velocity along the straight line .Again from Newton's law it would continue to move with uniform
  • This inherent property by virtue of which a body in state of uniform motion tend to maintain its uniform motion is called inertia of motion
  • Combining these two statements 'The property of an object to remain in state of rest or uniform rectilinear motion unless acted upon by a force is called inertia'
  • Mass of any body is the measure of inertia .For example if we apply equal amount of force on two objects of different mass (say m1 and
    m2 such that m1 > m2 ) then acceleration of both the object would be different (i.e , a1 < a2 )
  • Acceleration of object having larger mass would be lesser then the acceleration of object having smaller mass
  • Thus larger the mass of the body ,smaller would be the acceleration and larger would be the inertia
  • Newton's first law of motion revealing this fundamental property of matter i.e inertia is also known as law of inertia

(5) Newton's second law of motion

  • Newton's first law of motion qualitatively defines the concept of force and the principle of inertia
  • For an body at rest, application of force causes a changed in its existing state and application of force on a body moving with uniform velocity would give the body under consideration as acceleration
  • Newton's second law of motion is a relation between force and acceleration
  • Newton's second law of motion says that
    " The net force on a body is equal to the product of mass and acceleration of the body"
    Fnet=ma                               (1)
    Where Fnet is the vector sum of all the forces acting on the body
  • Above equation -(1) can be resolved along x,y and z components .Thus in component form
  • Component of acceleration along a given axis is caused only by the net component of force along that axis only not by the components of force along other axis
  • Newton's second law of motion is completely consistent with newton first law of motion as from equation (1) F=0 implies that a=0
  • For a body moving under the influence of force, acceleration at any instant is determined by the force at that instant not by the previous motion of the particle
  • Newton's second law of motion is strictly applicable to a single particle .In case of rigid bodies or system of particles, it refers to total external forces acting on the system excluding the internal forces in the system.

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