A thin uniform rod, pivoted at $O$, is rotating in the horizontal plane with constant angular speed $\omega$, as shown in the figure. At time, $t = 0$, a small insect starts from $O$ and moves with constant speed $v$ with respect to the rod towards the other end. It reaches the end of the rod at $t = T$ and stops. The angular speed of the system remains $\omega$ throughout. The magnitude of the torque $(|\overleftarrow{ au}|$ on the system about $O$, as a function of time is best represented by which plot [image:7_image42.emf]

Question

A thin uniform rod, pivoted at $O$, is rotating in the horizontal plane with constant angular speed $\omega$, as shown in the figure. At time, $t = 0$, a small insect starts from $O$ and moves with constant speed $v$ with respect to the rod towards the other end. It reaches the end of the rod at $t = T$ and stops. The angular speed of the system remains $\omega$ throughout. The magnitude of the torque $(|\overleftarrow{	au}|$ on the system about $O$, as a function of time is best represented by which plot [image:7_image42.emf]

Dr. Abubacker · Accepted Answer

(b) Angular momentum about rotational axis
$L_{t} = \lbrack I + m(vt)^{2}brack\omega$
$\frac{dL_{t}}{dt} = 2mv^{2}t\omega;$
Torque $	au = (2mv^{2}\omega)t$
[image:7_image133.emf]

Explanation

Reviewed by Dr. Abubacker

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