Answer :
The motor makes approximately 31.25 revolutions in 5.00 s as its angular velocity decreases uniformly from 600 to 150 rev/min.
To find the number of revolutions made by the motor in the 5.00 s interval, we first need to find the average angular velocity during this time period and then use it to calculate the number of revolutions.
Given:
Initial angular velocity, ω₁ = 600 rev/min
Final angular velocity, ω₂ = 150 rev/min
Time interval, t = 5.00 s
First, let's convert the initial and final angular velocities from rev/min to rev/s:
ω₁ = 600 rev/min = (600 rev/min) * (1 min / 60 s) = 10 rev/s
ω₂ = 150 rev/min = (150 rev/min) * (1 min / 60 s) = 2.5 rev/s
Now, we can find the average angular velocity (ω_avg) during the 5.00 s interval:
ω_avg = (ω₁ + ω₂) / 2
ω_avg = (10 rev/s + 2.5 rev/s) / 2
ω_avg = 6.25 rev/s
The number of revolutions made by the motor during the 5.00 s interval can be calculated using the formula:
Number of revolutions = ω_avg * t
Substituting the values:
Number of revolutions = 6.25 rev/s * 5.00 s = 31.25 revolutions
So, the motor makes approximately 31.25 revolutions in the 5.00 s interval.
