Final answer:
To solve for the angular velocity (ω) of the flywheel, we first determine the translational kinetic energy required for the bus, then find the total rotational energy the flywheel must have, considering 90% efficiency. Calculating the moment of inertia (I) for the flywheel allows us to solve for ω using the rotational kinetic energy formula. Which, when solved, can be compared to the given answer options.
Step-by-step explanation:
The student has asked to calculate the angular velocity the flywheel must have for a given situation. First, we find the translational kinetic energy needed to accelerate the bus to 20.0 m/s using the formula KEtrans = 1/2 m v2, where m is the mass of the bus and v is the velocity. Next, we calculate the total rotational energy (KErot) the flywheel must have, which is 1/efficiency times the translational kinetic energy needed, because only 90% of the rotational kinetic energy is converted to translational energy. Then we use the formula for rotational kinetic energy, KErot = 1/2 I ω2, where I is the moment of inertia of the flywheel (for a disk, I = 1/2 mf r2), and ω is the angular velocity.
By solving for ω, we can find the angular velocity the flywheel needs. Here's the calculation:
- KEtrans = 1/2 * 10,000 kg * (20 m/s)2
- KErot = KEtrans / 0.9
- I = 1/2 * 1500 kg * (0.600 m)2
- ω2 = (2 * KErot) / I
Solving for ω gives the correct angular velocity which can be matched to the given options for the answer.