Question

Define angular momentum and show the rate of change of angular momentum is equal to the torque

Answer 1

Answer:

the quantity of rotation of a body, which is the product of its moment of inertia and its angular velocity.

Explanation:

THEOREM:

The rate of change of the total angular momentum of a system of particles is equal to the sum of the external torques on the system.

Thus:

L=∑iri×pi(3.11.1)

∴L˙=∑ir˙i×p˙i(3.11.2)

But the first term is zero, because r˙ and pi are parallel.

Also

r˙i=Fi+∑Fij(3.11.3)

L˙i=∑iri×(ri+∑jFij)=∑iri×Fi+∑iri×∑jFii

∴∑iri×Fi+∑iri×∑jFii

But ∑i∑jFij=0 by Newton’s third law of motion, and so ∑i∑jri×Fij=0 .

Also ∑iri×Fi=τ , and so we arrive at

L˙=τ(3.11.4)

which was to be demonstrated.