Question

define angular momentum and torque .derive relation b/w them.

Answer 1

Angular momentum
L
L:- It is an measure of the rotation of body, taking into account its mass , shape and speed.

L = r ×â p
where r is distance from the axis of rotation and the p is the linear momntum of the body.

Torque
τ
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
1
where I is the moment of inertia of the body about an axis of rotation.

α
α is the angular acceleration.
We know for the rotational body angular momentum is conseverd. L = Iω ----- 2
2

where
ω
ω is the angular velocity.

As we know

α =  dω/dt ----3
3

taking derivative of equqtion no.
2
2 with respect to time, we get.
dL/dt = dω/dt ----4

4

using
3 &4

, we get.
dL/dt = Iα ---- 5


compare equation no

1 & 5
, we get.

ττ= dL/dt

This is the relationship between torque and angular momentum.


hope its helps

Answer 2

 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.
We have shown that Newton's second law can be written as

ΣF = dp/dt.

where ΣF is the net force acting on a body.  Thus we can write

r ´ ΣF = r ´ dp/dt.

Since the net torque acting on a body is Στ = r ´ ΣF, and since we can add to the right hand side of the preceding equation the quantity dr/dt ´ p = 0 without changing its value, we can write

Στ = r ´ dp/dt + dr/dt ´ p = d(r ´ p)/dt.

We define angular momentum as

 L º r ´ p

The preceding equation then becomes

Στ = d L/dt,

which is the rotational analogue of Newton's second law as expressed at the top of this derivation.  (We note that 
like torque, which depends both upon the net force applied to a body and the point about which that torque is 
calculated, a body's angular momentum depends upon the net momentum of the body and upon the point about 
which its angular momentum is calculated.)

Hope it helps you buddy..
Cheers!!