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An engineer is testing a large wind turbine that is used generating energy. Intially the large wind blades are locked in place and not rotating. In a steady wind, the engineer releases the blades and they begin to rotate. She notes from the instruments that for the first 60 seconds the blades have a constant angular acceleration of 0.05rad/s2 . How many complete revolutions of the turbine occur during this time

Respuesta :

Answer:

3 revolution in rad

Explanation:

angular acceleration α= rev/time

but α= 0.05rad/s

rev = α * time(in sec)

rev = 0.05 * 60

rev = 3rad/s

xero099

The turbine completed about 14 revolutions for the first 60 seconds.

How to calculate the revolutions done by a wind turbine rotating at constant acceleration

The number of revolutions ([tex]\Delta n[/tex]) completed by the turbine is found by the following formula:

[tex]\Delta n = \frac{\omega_{o}\cdot t+0.5\cdot \alpha\cdot t^{2}}{2\pi}[/tex] (1)

Where:

  • [tex]\omega_{o}[/tex] - Initial angular speed, in radians per second.
  • [tex]t[/tex] - Time, in seconds.
  • [tex]\alpha[/tex] - Angular acceleration, in radians per square second.

If we know that [tex]\omega_{o} = 0\,\frac{rad}{s}[/tex], [tex]t = 60\,s[/tex] and [tex]\alpha = 0.05\,\frac{rad}{s^{2}}[/tex], then the number of revolutions completed by the wind turbine is:

[tex]\Delta n = \frac{(0)\cdot (60)+0.5\cdot (0.05)\cdot (60)^{2}}{2\pi}[/tex]

[tex]\Delta n = 14.324\,rev[/tex]

The turbine completed about 14 revolutions for the first 60 seconds. [tex]\blacksquare[/tex]

To learn more on angular motion, we kindly invite to check this verified question: https://brainly.com/question/21482828

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