Question

relation between torque and angular momentum.(derive)

Answer 1

Angular momentum(L):-  It is an measure of the rotation of body, taking into account its mass , shape and speed.
 
L =  r ×​ p
where r is distance from the axis of rotation and the p is the linear momntum of the body.

Torque(τ): It is an moment of force i.e. tendency of a force to rotate an object about an axis.

τ = r × f 
where r is the perpendicular distance from the axis of the rotation and f is the applied force.
 
For rotational motion torque is given by:
τ = Iα ----- (1)
where I is the moment of inertia of the body about an axis of rotation.
         α is the angular acceleration.
We know for the rotational body angular momentum is conseverd. L = Iω ----- (2)

where ω is the angular velocity.
 
As we know 
α =  dω/dt ----(3)
 
taking derivative of equqtion no. (2) with respect to time, we get.
dL/dt = Idω/dt  ----(4)

using (3) &(4), we get.
 dL/dt = Iα ---- (5)

compare equation no (1) & (5), we  get.

τ= dL/dt
This is the relationship  between torque and angular momentum. 

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