JEE Advanced 2012 Paper 1 Physics Q1

Physics · Rotation

Problem

A thin uniform rod, pivoted at OO, is rotating in the horizontal plane with constant angular speed ω\omega, as shown in the figure. At time t=0t=0, a small insect starts from OO and moves with constant speed vv with respect to the rod towards the other end. It reaches the end of the rod at t=Tt=T and stops. The angular speed of the system remains ω\omega throughout. The magnitude of the torque (∣τ⃗∣)(|\vec{\tau}|) on the system about OO, as a function of time is best represented by which plot?
Intuitive explanation

The key is recognizing that torque depends on both the insect's distance from the pivot and the forces needed to keep it moving in the rotating frame. As the insect crawls outward at constant speed vv relative to the rod, its distance from OO increases linearly: r(t)=vtr(t) = vt. The torque has two sources: the tangential force needed to accelerate the insect in the rotating frame (which grows with rr), and the Coriolis-like effects. Since rr increases linearly with time, the net torque magnitude grows linearly from zero at t=0t=0 to a maximum at t=Tt=T, then drops to zero when the insect stops moving relative to the rod.

Intuitive explanation

The key is recognizing that torque depends on both the insect's distance from the pivot and the forces needed to keep it moving in the rotating frame. As the insect crawls outward at constant speed vv relative to the rod, its distance from OO increases linearly: r(t)=vtr(t) = vt. The torque has two sources: the tangential force needed to accelerate the insect in the rotating frame (which grows with rr), and the Coriolis-like effects. Since rr increases linearly with time, the net torque magnitude grows linearly from zero at t=0t=0 to a maximum at t=Tt=T, then drops to zero when the insect stops moving relative to the rod.

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