Question

Mention the relation between torque and angular momentum of a body

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.

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Answer 2

Answer:

We know :

τ = F × d x .

Kinematics and dynamics are have common analogy .

As in Kinematics there is Force there here in dynamics there is torque .

Linear momentum here angular momentum.

We know :

F =  d P / d t

Here :

τ = d L / d t

Where L is angular momentum and t is time .