A uniform rod of length ' ℓ ' is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω the rod makes an angle θ with it (see figure). To f

Question

A uniform rod of length ' ℓ ' is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed ω the rod makes an angle θ with it (see figure). To find θ equate the rate of change of angular momentum (direction going into the paper) m ℓ 2 12 ω 2 sin θ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces F H and F v about the CM. The value of θ is then such that:

TestHub · Accepted Answer

Torque of centrifugal force τ cf = dm . x sin θω 2 xcos ϑ = m l ω 2 sin θcos θ ∫ 0 l x 2 dx τ ef = m l 2 ω 2 sinθ cosθ 3 τ mg = τ cf mg . l 2 sin θ = m l 2 ω 2 sinθ cos θ 3 cos θ = 3 g 2 l ω 2

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion