A laboratory uses wheels to supply the electrical power that is needed to ignite plasma.
Suppose each wheel has a mass of m=610 tonnes. At full speed, the rotation rate is 270 revolutions per minute and the wheel stores an energy of k=3.8 GJ. Assume that it is a solid cylinder of uniform density. (a) Calculate the wheel's moment of inertia. (b) Calculate the wheel's radius. (c) Calculate the linear speed of a point on the wheel's rim. (d) Calculate the centripetal acceleration of a point on the wheel’s rim. (e) To release the energy, the wheel is spun down over a period of T=9.00 s. Calculate the average torque that must be applied during this time (which will be a negative number, since the wheel is decelerating). (f) The wheel's axle disintegrates and, without losing energy, it begins rolling through the laboratory. Calculate its linear speed. (g) The flywheel encounters a gently sloping ramp. Calculate the height of the ramp that is just sufficient to stop its motion.