Question

At t = 0, a flywheel has an angular velocity of 6.1 rad/s, an angular acceleration of -0.13 rad/s2, and a reference line at θ0 = 0. (a) Through what maximum angle θmax will the reference line turn in the positive direction? What are the (b) first and (c) second times the reference line will be at θ = θmax/6? At what (d) negative time and (e) positive time will the reference line be at θ = -11 rad?

Answer 1

Time before starting the reference line turn is $t_0=\omega_0/\beta\approx47s$ where $\omega_0=6.1rad/s,\beta=0.13rad/s^2$ then

(a) $\Theta_{max}=\int_{0}^{t_0}(\omega_0-\beta t^2/2)dt\approx143rad$

(b),(c) If $\Theta=\Theta_{max}/6\approx23.8rad$ , as $\Theta=\omega_0t-\beta t^2/2$ hence $t_1\approx90s,t_2\approx4s$

(d),(e) If $\Theta=-11rad$ then we get $t_1\approx-2s,t_2\approx96s$