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Answer:
The time of motion is 333.3 s
The angular acceleration is -0.0045 rad/s²
Explanation:
Given;
angular distance of the flywheel, θ = 40 rev
initial angular speed, [tex]\omega_i[/tex] = 1.5 rad/s
When the wheel comes to rest, the final angular speed, [tex]\omega_f[/tex] = 0
The angular acceleration is calculated as follows;
[tex]\omega_f^2 = \omega_i^2 + 2\alpha \theta \\\\0 = (1.5 \ rad/s)^2 + 2\alpha (40 \ rev\times \frac{2\pi \ rad}{1 \ rev} )\\\\0 = 2.25 + 160\pi \alpha\\\\160\pi \alpha = - 2.25\\\\\alpha = -\frac{2.25 }{160\pi} \\\\\alpha = -0.0045 \ rad/s^2[/tex]
The time of motion is calculated as;
[tex]\omega_f = \omega _i + \alpha t\\\\0 = 1.5 + (-0.0045t)\\\\0 = 1.5 - 0.0045t\\\\0.0045t = 1.5\\\\t = \frac{1.5}{0.0045} = 333.3 \ s[/tex]