A flywheel has a moment of inertia of 2.6 kg·m2. What is the average power needed to spin it up from rest to an angular velocity of 100 rad/s in 30 seconds?
power= work/time= energy/time= 1/2 I w^2/time
Thank you for your help!
To calculate the average power needed to spin up the flywheel, we can use the formula:
Average power = (Change in rotational energy) / (Change in time)
The change in rotational energy is given by the formula:
Change in rotational energy = (1/2) * (moment of inertia) * (final angular velocity^2 - initial angular velocity^2)
Given:
Moment of inertia (I) = 2.6 kg·m^2
Final angular velocity (ωf) = 100 rad/s
Initial angular velocity (ωi) = 0 rad/s
Change in time (Δt) = 30 s
Now, let's calculate the change in rotational energy:
Change in rotational energy = (1/2) * (2.6 kg·m^2) * ((100 rad/s)^2 - (0 rad/s)^2)
= (1/2) * (2.6 kg·m^2) * (10000 rad^2/s^2 - 0 rad^2/s^2)
= (1/2) * (2.6 kg·m^2) * 10000 rad^2/s^2
= 13000 N·m
Next, we'll calculate the average power:
Average power = (Change in rotational energy) / (Change in time)
= 13000 N·m / 30 s
≈ 433.33 W
Therefore, the average power needed to spin up the flywheel from rest to an angular velocity of 100 rad/s in 30 seconds is approximately 433.33 Watts.