A rotating platform in a laboratory undergoes the following single-cycle…

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A rotating platform in a laboratory undergoes the following single-cycle angular-acceleration program in order to test sensors mounted on its edge. The angular acceleration α(t)\alpha(t) varies linearly with time: • From t=0 st = 0\,\text{s} to t=4 st = 4\,\text{s}, α\alpha increases uniformly from 0 rad/s20\,\text{rad/s}^2 to +2 rad/s2+2\,\text{rad/s}^2. • From t=4 st = 4\,\text{s} to t=7 st = 7\,\text{s}, α\alpha decreases uniformly to −4 rad/s2-4\,\text{rad/s}^2. • From t=7 st = 7\,\text{s} to t=10 st = 10\,\text{s}, α\alpha increases uniformly back to 0 rad/s20\,\text{rad/s}^2. At t=0 st = 0\,\text{s} the platform is at rest, and its angular position is defined to be θ=0\theta = 0. Counter-clockwise is positive. (a) Determine the angular velocity ω\omega at t=4 st = 4\,\text{s}, at t=7 st = 7\,\text{s}, and at t=10 st = 10\,\text{s}. Clearly show how you obtain each value. (b) On separate, clearly labeled axes, sketch qualitatively accurate graphs of ω\omega versus tt and θ\theta versus tt for the entire 0–10 s interval. Label any local maxima or minima on your θ(t)\theta(t) graph. (c) Calculate the total angular displacement of the platform over the full 10 s interval. (d) Does the platform rotate clockwise at any time during the 10 s program? Support your conclusion with quantitative evidence.

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