A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed ω, 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. If reaches the end of the rod at t = T and stops. The angular speed of the system remains ω throughout. The magnitude of the torque on the system about O, as a function of time is best represented by which plot?

Engineering

Physics

Angular Momentum and Conservation of Angular Momentum

Question

A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed ω, 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. If reaches the end of the rod at t = T and stops. The angular speed of the system remains ω throughout. The magnitude of the torque $(| \vec{τ} |)$ on the system about O, as a function of time is best represented by which plot?

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$τ = \frac{dL}{dt} = \frac{d}{dt} (l + {mx}^{2}) ω = m \times 2 x \frac{dx}{dt} ω = 2 {mωv}^{2} t [as x = vt]$