Hello! Can you provide response to each part of the problem by using physics concepts or formulas? Please also provide all math/formula/conceptual steps so that I can check my own work. This question involves Physics Conversions, Conservation of Energy, Potential Energy, Kinetic energy, Work-energy Theorem, etc.

Flywheel-based regenerative braking Reference Information: W'e've dealt with regenerative braking, where electric. vehicles convert kinetic energy into chemical energy of the battery. But sometimes the required power is too great for batteries. Consider the San Diego Metro Rail rapid transit (subway) trains weighing 216.000 kg with six empty cars that come to a stop in a matter of seconds. Lithium-ion batteries don't charge that quickly. so if you want to conserve that energy, you need something else. You can't send a power spike of that size to the electrical grid. so how do you store that energy? Enter the. ywheel: any spinning wheel. disk. or cylinder that stores rotational kinetic energy to he used later. In this case. the metro station has a bank of rotating cylinders that spin up to store the traiu's kinetic energy and spin down to accelerate them. Compared to batteries. flywheels last. much longer with no degradation of capacity. require no toxic or rare materials. operate in a wider temperature range. and require minimal maintenance. Their drawback is their high cost per unit energy stored. Specications of the train: mass of G-ear train is 210.000 kg. maximum acceleration and deceleration is i1.35n1/s, average speed before braking is 30mph. Specifications of the ywheel system: 16 identical cylindrical drums with a mass of 500 kg and a radius of 9cm. The. ywheels have a minimum operating angular speed of 10.000 rpm. This is their \"fully discharged" state: they spin up to store more energy. Assume all 16 ywheels are synced so that they always spin with the same. angular speed. Practice Problem: (a) What power (in MW") is required to stop a. train at 30 mph? (1)) How much energy (in kWh) is stored in one braking cycle? (c) Starting from 10,000 rpm. how fast do the ywheels spin up to store this energy? Reference Figure: The two cylinders in the middle of the cabinet are the containment vessels for the ywheels