Question

relation between torque and angular momentum

Answer 1

When a torque is applied to an object it begins to rotate with an acceleration inversely proportional to its moment of inertia.

This relation can be thought of as Newton’s Second Law for rotation. The moment of inertia is the rotational mass and the torque is rotational force.

Angular motion obeys Newton’s First Law. If no outside forces act on an object, an object in motion remains in motion and an object at rest remains at rest.

Key Terms

angular acceleration: The rate of change of angular velocity, often represented by α.

torque: A rotational or twisting effect of a force; (SI unit newton-meter or Nm; imperial unit foot-pound or ft-lb)

rotational inertia: The tendency of a rotating object to remain rotating unless a torque is applied to it.

Torque and angular acceleration are related by the following formula where is the objects moment of inertia and αα is the angular acceleration.

Answer 2

Hey !!

We know that,

Torque,           τ = r × F

Angular momentum,     L = r × p

On differentiating both sides w.r.t time t, we get

         dL/dt = d/dt (r × p) = dr/dt × p × r × dp/dt

          = v × p + r × F                      [∴ dp/dt = F]

            = 0 + τ

∵              τ = dL/dt

Thus, the torque acting on a particle is equal to its rate of change of angular momentum.

Good luck !!