Answer:
a)
b) the rotational acceleration will remain the same,
c) When r = 36 m,
When r = 18 m,
d) When r = 36 m,
When r = 36 m,
Explanation:
The windmills are spinning 20 times per minute, the number of spins in 1 second = 20/60 = 1/3 spins/sec
frequency, f = 1/3 spins/sec
there are 1/3 spins in 1 second,
there will be 50 spins in 50/ (1/3) seconds = 150 seconds
i.e time taken to make 50 spins = 150 seconds
Time interval between 20 and 50 spins, Δt = 150 - 60 = 90
Δt = 90
Angular frequency at 20 spins:
w₁ = 2 π f
w₁ = 2 π * 1/3 = 2π/3 = 2.09 rad/s
Since the blade stops at 50 spins, angular frequency at 50 spins, w₂ = 0
The rotational acceleration,
b) The magnitude of the rotational acceleration does not depend on the radius, r. It depends on the angular frequency, therefore the magnitude of the rotational acceleration doe not change.
c) The centripetal acceleration is given by the formula,
While the windmill spins at 20 times per minute, the angular speed gotten, w = 2.09 rad/s
When r = 36 m
At the halfway point, r = 18 m
d) If the angular velocity of the blades were cut in halves:
w = 2.09/2
w = 1.045 rad/s
When r = 36 m
When r = 18 m