Question

what do you understand by the angular momentum of particle? driver relation between angular momentum of a particle nad torque acting on it

Answer 1

Angular momentum :- angular momentum is the cross product of separation between observation point to axis of rotation of object and linear momentum of object . Mathematically , $\bold{L=r\times P}$ , here r is the separation between observation point to axis of rotation and P is the linear momentum of object. or, $\bold{L=r\times mv}$ or, $\bold{L=m(r \times v)}$

we know, torque is the cross product of separation between observation point to axis of rotation and Force act on object .
e.g., τ = r × F = r × ma [ ∵ Newton's 2nd law , F = ma ]
τ = m( r × a)
τ = m( r × dv/dt ) [ ∵ acceleration is rate of change of velocity , a = dv/dt]
τ = r × d(mv)/dt
τ = r × dP/dt [ ∵ P = mv
τ = d(r × P)/dt = dL/dt
Hence, torque is the rate of change of angular momentum .