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A wind turbine is initially spinning at a constant angular speed. as the wind's strength gradually increases, the turbine experiences a constant angular acceleration 0.101 rad/s2. after making 2870 revolutions, its angular speed is 149 rad/s. (a) what is the initial angular velocity of the turbine? (b) how much time elapses while the turbine is speeding up?

Respuesta :

meerkat18
Let us list the given: 

constant acceleration = 0.101 rad/s^2
angular distance = 2870 revolutions 
*since 1 revolution = 2π rad, this is equal to 5740π rad (2870*2π)
angular speed = 149 rad/s

From here, we could infer that it is easier to determine letter b first. To solve for time, just divide distance by speed

b.) time = 5740π/149 rad/s = 121.03 seconds

a.) For letter a, we use the formula for acceleration

a = (v,final - v,initial)/t
0.101 rad/s^2= (149 rad/s - v,initial)/121.03 s
v,initial = 136.78 rad/s
asuwafohjames

(a) The initial angular speed of the turbine is 136.22 rad/s

(b) The amount of time that will elapse while the turbine is speeding up is 126.53 seconds

What is angular velocity?

Angular velocity is the rate of change of angular displacement with time.

The S.I unit is rad/s.

(a) To calculate the initial angular velocity of the turbine, we apply the formula below.

Formula:

  • ω² = ω'²+2∅α................. Equation 1

Where:

  • ω = Final angular speed
  • ω' = Initial angular speed
  • ∅ =  Angular rotation
  • ∝ = Angular acceleration.

From the question,

Given:

  • α = 0.101 rad/s²
  • ω = 149 rad/s
  • ∅ = 2870 rev = 2870(2π) = 18040 rad

Substitute these values into equation 1 and solve for ω'

  • 149² = ω'²+(0.101×2×18040)
  • 22201 = ω'²+
  • ω'² = 22201-3644.08
  • ω'² =
  • ω' = √(18556.92)
  • ω' = 136.22 rad/s.

(b) Also to calculate the amount of time that will elapse while the turbine is speeding up, we use the formula below.

Formula:

  • t = (ω-ω')/α............... Equation 2

Where:

  • t = Time

Substitute into equation 2

  • t = (149-136.22)/0.101
  • t = 12.78/0.101
  • t = 126.53 seconds.

Hence, (a) The initial angular velocity of the turbine is 136.22 rad/s (b) The amount of time that will elapse while the turbine is speeding up is 126.53 seconds

Learn more about angular velocity here: https://brainly.com/question/9408577

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