Flywheels are large, massive wheels (solid cylinders) used to store energy. they can be spun up slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. an industrial flywheel has a radius of r = 1 m and a mass of m = 250 kg. it’s maximum angular velocity is ωmax = 1200 rpm.

(i) concept question. power is the energy output per unit time. it’s measured in joules per second, or "watts" (w). if you have two processes that expend the same energy e, but take different times. process (1) takes time t and process (2) takes time t/2. which process is higher power?

(ii) a motor spins up the flywheel with a constant torque of τspinup = 50 nm. how much time tspinup does it take to speed up to ωmax. find an expression in terms of ωmax, m, and r. then substitute numbers; you should get 314 s.

(iii) how much energy emax is stored in the fly wheel when it is spinning with its maximum velocity? express your answer in terms of ωmax, m, and r. then substitute numbers; you should find 986960 j.

(iv) the flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. half the energy stored in the flywheel is delivered in tspindown = 2.0 s. what is the average power pavg delivered to the machine? find an expression in terms emax and tspindown and then substitute numbers: you should get 246740 w.

(v) how much torque τspindown does the flywheel exert on the machine? assume constant torque and find your answer in terms of ωmax, m, r, and tspindown. then substitute numbers. the numerical answer is 2300 nm.