Answer:
A) t = 1.249 10⁻² s, B) f = 80 Hz, C) f = 20 Hz,
D) slowly advancing an angle of approximately Δθ = 0.05 rad each flash
E) In each flash it seems to go backward an angle of Δθ = -0.05 rad
Explanation:
A) To make it appear that the blades are immobile, it implies that every time the light turns on, a blade should be in the same position, therefore, as we have 4 blades, they must rotate an angle of 2π/4,
θ = π / 2
θ = 1.57 rad
taking the angle let's use the endowment kinematics relations
θ = w₀ t + ½ α t²
in general the fans rotate at constant speed α= 0
θ = w₀ t
t = θ / w₀
let's reduce the magnitudes to the SI system
w₀ = 20 rev / s (2π rad / 1rev) = 125.66 rad / s
let's calculate
t = 1.57 / 125.66
t = 1.249 10⁻² s
B) the fastest speed for the blades to rotate is when one blade of a complete turn , we use the relationship between the fecuance and the period
f = 1 / T
f = 1 / 1.25 10⁻²
f = 80 Hz
C) we have two possibilities:
* a yellow dot is placed on each sheet
In this case the angular velocity of the blade is the same at all points, therefore the results obtained should not change
* a yellow dot is placed on a single sheet.
Here for the point to remain fixed the angle of rotation must be
θ= 2π rad
the time is
t = 2π / 125.66
t = 5 10⁻² s
the maximum frequency is
f = 1/5 10⁻²
f = 20 Hz
D) The copy strobe rotates at f = 19 Hz, the time between each flash is
t = 1/19
t = 5.26 10⁻² s
this time is higher, so the angle turned is large
θ = w t
θ = 125.66 5.26 10⁻²
θ = 6.61 rad
the relationship between this angle and the angle of a circle is
θ = 1,052
We can see that it is this time the blade rotates 1 complete turns, for this the position of the blade changes us, for the other 0.052 rad the blade rotates a little more than the circumference therefore it seems that it is slowly advancing an angle of approximately
Δθ = 0.05 rad each flash
E) in this case changes the flash speed
t = 1/21
t = 4.76 10⁻² s
the angle rotated is
θ = 125.66 4.76 10⁻²
θ = 5.984 rad
θ / 2π = 0.95
in that case, the blade did not complete the turn, therefore in each flash it seems to go backward an angle
Δθ = -0.05 rad
