Question

derive the relationship 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.

Answer 2

Answer:

Explanation:

The relationship between torque and angular momentum can be derived from Newton's second law for rotational motion. The equation for torque is given by:

τ = I * α,

where τ is the torque, I is the moment of inertia and α is the angular acceleration.

The equation for angular momentum is given by:

L = I * ω,

where L is the angular momentum and ω is the angular velocity.

Taking the derivative of angular momentum with respect to time, we have:

dL/dt = d(I * ω) / dt = I * dω/dt = I * α

Comparing this with the equation for torque, we see that:

dL/dt = τ

So the derivative of angular momentum with respect to time is equal to the torque applied to an object. This relationship between torque and angular momentum states that a torque applied to an object will cause a change in its angular momentum.