A cylinder weighing 450 N with a radius of 30 cm is held fixed on an incline that is rotating at 0 . 5 rad s - 1 . The cylinder is released when the incline is at position θ equal to 30 ° . If the cyl

Question

A cylinder weighing 450 N with a radius of 30 cm is held fixed on an incline that is rotating at 0 . 5 rad s - 1 . The cylinder is released when the incline is at position θ equal to 30 ° . If the cylinder is 6 m from the bottom A at the instant of release, what is the initial acceleration of the centre of the cylinder relative to the incline, if there is no slipping? g = 10 m s - 2

TestHub · Accepted Answer

Free body diagram of the cylinder w.r.t. the inclined plane. The torque about the point of contact O.

$(mg sin θ - mr ω^{2}) R = I . α = \frac{3}{2} {mR}^{2} \times \frac{a}{R}$ ( $r$ = radius of circle, $R = 6 m$ )

$∴ mgsin θ - mr ω^{2} = \frac{3}{2} ma$

$∴ a = \frac{2}{3} (g sin θ - r ω^{2}) = \frac{2}{3} [10 \times \frac{1}{2} - 6 \times \frac{1}{4}] = 2.33 {m s}^{- 2}$

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