A cylinder rests on a horizontal rotating disc, as shown in the figure. The distance between the axes of the disc and cylinder is R, and the coefficient of friction \mu > \frac{D}{h}, where D is the diameter of the cylinder and h is its height. The angular velocity at which cylinder topples and falls off the disc is _____ × 10–2 rad/sec. (Given R = 4D, h = 4D, D = 10m)

Engineering

Physics

Static and Kinetic Friction

Free Body Diagram

Centripetal and Centrifugal Force

Question

A cylinder rests on a horizontal rotating disc, as shown in the figure. The distance between the axes of the disc and cylinder is R, and the coefficient of friction $μ > \frac{D}{h}$ , where D is the diameter of the cylinder and h is its height. The angular velocity at which cylinder topples and falls off the disc is _____ × 10^–2 rad/sec. (Given R = 4D, h = 4D, D = 10m)

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Cylinder will topple about right bottom

$\frac{h}{2} {mw}^{2} R \geq \frac{D}{2} mg$

$w^{2} \geq \frac{Dg}{Rh}$

$w_{min} = \sqrt{\frac{Dg}{Rh}}$