Rate Of Change Of Momentum
Momentum of a body is the product of its mass and velocity.when a force is applied on a moving body
,its velocity changes.Due to changes in velocity of the body,its momentum changes and it is called rate of change of momentum.
In classical mechanics, linear momentum or translational momentum (pl. momenta; SI unit kg m/s, or, equivalently, N s) is the product of the mass and velocity of an object. For example, a heavy truck moving fast has a large momentumit takes a large and prolonged force to get the truck up to this speed, and it takes a large and prolonged force to bring it to a stop afterwards. If the truck were lighter, or moving slower, then it would have less momentum.
Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude: p = mv.
Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. In classical mechanics, conservation of linear momentum is implied by Newton's laws; but it also holds in special relativity (with a modified formula) and, with appropriate definitions, a (generalized) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity.
Linear Momentum: Rate of Change of Momentum
It is our common experience that if two bodies of different masses are moving with the same velocity, the force needed to stop the heavier body is more than that for the lighter body. similarly,if two bodies of the same masses are moving with different velocities,the force needed to stop the faster moving body is more than the slower moving body.Thus,the force needed to stop a moving body de3pends both on the mass of the body and its velocity.
actually the force needed to stop a moving body depends on the product of both mass and velocity.the product of mass and velocity of a moving body is called its linear momentum.
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The linear momentum of a body is denoted by the letter 'p'.Quite often the word momentum is used for linear momentum.
For a body of mass m moving with velocity v ,linear momentum p is expressed as- p=mv.
It is a vector quantity.it is in direction of motion of the body (i.e. the velocity body).
UNIT:
Unit of momentum=unit of mass*unit of velocity. The S.I. unit of momentum is kg m s^-1 and the C.G.S. unit is g cm s^-1.
Definition of Rate of Change of Momentum
when a force is applied on a moving body,its velocity changes.Due to changes in velocity of the body,its momentum changes and it is called rate of change of momentum.
Let a force F acts on a body of mass m for time t and changes its velocity from u to v.Then,
initial momentum of body=mu
final momentum of body=mv
change in momentum of body in t seconds=mv-mu=m(v-u).
rate of change of momentum=change in momentum/time=m(v-u)/t.
but acceleration a=v-u/t
therefore,rate of change of momentum=ma
=mass*acceleration.......(1)
Thus when a force acts on a body,the rate of change in momentum of body is equal to the product of mass of the body and acceleration produced in it due to that force.The relation (1) holds when mass of the body remains constant.
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