Question

what is the relation between torque and angular momentum? explain briefly

Answer 1

Answer:

Angular Momentum is the momentum experienced by a body during rotational motion. Torque is defined as the Force which is experienced during rotational motion.

According to Newton's Second Law,

Force = Mass × Acceleration

According to Rotational Motion,

Torque = Moment of Inertia × Angular Acceleration

⇒ τ = Iα

We know that, rate of change of Momentum is Force. Similarly, we can say that Torque is the rate of change of Angular Momentum.

Linear Momentum = m × v

Angular Momentum = m × r × v

⇒ Angular Momentum = m × ω ( w is the angular velocity )

But according to Rotational Dynamics, mass is considered to be Moment of Inertia which is denoted as I and is constant for same body.

Differentiating Angular Momentum with respect to time we get,

⇒ d ( I.ω ) / dt

⇒ i ( dω/dt )

⇒ Iα

Here, α is the angular acceleration and Iα is Torque.

Therefore the relation between Angular Momentum and Torque is given as: τ = d ( L ) / dt

Here, L is the Angular Momentum.

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 .