Answer :
The flywheel turns through 3600 revolutions during the given interval.
To determine the number of revolutions the flywheel turns during the given interval, we can use the formula for average angular velocity:
Average angular velocity (ω_avg) = Δθ / Δt,
where Δθ is the change in angle (in radians) and Δt is the change in time (in seconds).
First, we need to convert the initial and final speeds from revolutions per minute (rev/min) to radians per second (rad/s).
Given:
Initial speed (ω_i) = 300 rev/min
Final speed (ω_f) = 900 rev/min
Time interval (Δt) = 6 seconds
To convert the speeds to rad/s, we can use the conversion factor: 1 rev/min = 2π rad/min.
Converting the initial and final speeds:
ω_i = 300 rev/min * (2π rad/min) = 600π rad/s
ω_f = 900 rev/min * (2π rad/min) = 1800π rad/s
Next, we can calculate the change in angular velocity (Δω) by subtracting the initial angular velocity from the final angular velocity:
Δω = ω_f - ω_i = 1800π rad/s - 600π rad/s = 1200π rad/s
Now, we can use the average angular velocity formula to find Δθ:
ω_avg = Δθ / Δt
Solving for Δθ:
Δθ = ω_avg * Δt
Since the problem states that the acceleration is uniform, the average angular velocity (ω_avg) can be calculated by taking the average of the initial and final angular velocities:
ω_avg = (ω_i + ω_f) / 2 = (600π rad/s + 1800π rad/s) / 2 = 1200π rad/s
Substituting the values into the formula:
Δθ = (1200π rad/s) * (6 s) = 7200π rad
Finally, to convert the change in angle from radians to revolutions, we divide Δθ by 2π:
N = Δθ / (2π) = 7200π rad / (2π) = 3600 revolutions
Therefore, the flywheel turns through 3600 revolutions during the given interval.
Learn more about revolutions here
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