Torque on a rotating system system

[Saptarshi Sarkar]

Homework Statement

A thin massless rod of length 2l has equal point masses m attached at its ends (see
figure). The rod is rotating about an axis passing through its centre and making angle θ with it. What is the magnitude of the rate of change of its angular momentum?

Relevant Equations

$L=Iω$
$τ=Iα=\frac {dL}{dt}$

I calculated the total moment of inertia of the system to be $2ml²Sin²θ$, so the angular momentum is $2ml²ωSin²θ$.

To get the torque on the system I need to differentiate the angular momentum but I don't have any time dependent terms. What should I do?

 

[TSny]

Your expression gives only the vertical component of angular momentum. You’re going to need the vector expression for the total angular momentum in order to see if the direction of angular momentum is changing.

So, use the vector definition of angular momentum for a point particle. Take the origin at the center of the rod.