JEE Main & Advanced Physics NLM, Friction, Circular Motion Newton's Second Law

(1) The rate of change of linear momentum of a body is directly proportional to the external force applied on the body and this change takes place always in the direction of the applied force.

(2) If a body of mass m, moves with velocity \[\vec{v}\] then its linear momentum can be given by\[\vec{p}=m\vec{v}\] and if force \[\overset{\to }{\mathop{F}}\,\] is applied on a body, then           

\[\vec{F}\propto \frac{d\vec{p}}{dt}\Rightarrow F=K\frac{d\vec{p}}{dt}\]

or \[\vec{F}=\frac{d\vec{p}}{dt}\]                         (K = 1 in C.G.S. and S.I. units)

or                 \[\vec{F}=\frac{d}{dt}(m\vec{v})=m\frac{d\vec{v}}{dt}=m\vec{a}\]       

(As \[a=\frac{d\vec{v}}{dt}=\]acceleration produced in the body)

\[\therefore \] \[\vec{F}=m\vec{a}\]   

Force = mass ´ acceleration