Answer:
a) 23.1 s
b) 68.1 rev
Explanation:
a) t = ω/α = 37.0 / 1.60 = 23.125 ≈ 23.1 s
ω₁² = ω₀² + 2αθ
θ = (ω₁² - ω₀²) / 2α = (37.0² - 0.00²) / 2(1.60) = 427.8125 radians
427.8125 rad / 2π rad/rev = 68.08847...
The time by the blade to given final angular speed is 23.125 seconds.
The number of revolutions made by the blade is 68 revolutions.
The given parameters;
The time of motion of the blade is calculated as follows;
[tex]\omega _f = \omega _i \ + \ \alpha t[/tex]
where;
[tex]\omega _i[/tex] is the initial angular speed = 0
[tex]37 = 0 + 1.6t\\\\t = \frac{37}{1.6} \\\\t = 23.125 \ s[/tex]
The number of revolutions made by the blade is calculated as follows;
[tex]\theta = (\frac{\omega _i + \omega _f}{2} )t\\\\\theta = (\frac{37}{2} )\times 23.125\\\\\theta = 427.81 \ rad\\\\\theta = 427.81 \ rad \times \frac{1 \ rev}{2 \pi \ rad} = 68 \ revolutions[/tex]
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