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

Step-by-step solution

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 = 3 2 mR 2 × a R ⁡ ( r = radius of circle, R = 6   m ) ∴ mgsin θ - mr ω 2 = 3 2 ma ∴ a = 2 3 g sin θ - r ⁡ ω 2 = 2 3 1 0 × 1 2 - 6 × 1 4 = 2 . 3 3 m s - 2