A wind turbine rotates at 8.40 rpm and has an angular acceleration of 0.0326 rad/s2. If the wind turbine takes 27.0 s to come to a complete stop, how many revolutions will this take?

avg speed=8.40rpm/2=4.10rpm

revolutions=avgspeed*time=4.1*(27sec/60sec)

r

To find the number of revolutions the wind turbine will take to come to a complete stop, we can use the equations of motion for rotational motion.

First, we need to find the initial angular velocity (ω0) of the wind turbine. We know that the wind turbine rotates at 8.40 rpm (revolutions per minute).

To convert this to radians per second, we need to multiply by 2π/60 (since there are 2π radians in one revolution and 60 seconds in one minute):

ω0 = 8.40 rpm × (2π/60) rad/s ≈ 0.8796 rad/s

Next, we can use the formula to calculate the final angular velocity (ωf) when the wind turbine comes to a complete stop:

ωf = ω0 + α × t

where α is the angular acceleration and t is the time taken for the wind turbine to come to a complete stop.

Plugging in the given values:

ωf = 0 + (0.0326 rad/s^2) × (27.0 s) ≈ 0.8814 rad/s

Now, we can use the formula to find the number of revolutions:

θ = (ω0 + ωf) × t/2π

where θ is the total angular displacement in radians.

Plugging in the values:

θ = (0.8796 rad/s + 0.8814 rad/s) × (27.0 s) / (2π) ≈ 39.46 radians

To convert this angular displacement to revolutions, we divide by 2π (since there are 2π radians in one revolution):

Number of revolutions = 39.46 radians / (2π) ≈ 6.28 revolutions

Therefore, the wind turbine will take approximately 6.28 revolutions to come to a complete stop.