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The rotating blade of a blender turns with constant angular acceleration 1.60 rad/s2.
(a) How much time does it take to reach an angular velocity of 37.0 rad/s, starting from rest? s
(b) Through how many revolutions does the blade turn in this time interval? rev

Sagot :

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...

Onyebuchinnajiidn

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;

  • angular acceleration of the blade = 1.6 rad/s²

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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