A car is designed to get its energy from a rotating flywheel (solid disk) with a

Question

A car is designed to get its energy from a rotating flywheel (solid disk) with a radius of 1.00 m and a mass of 400 kg. Before a trip, the flywheel is attached to an electric motor, which brings the flywheel's rotational speed up to 5,000 rev/min.
(a) Find the kinetic energy stored in the flywheel.
________J

(b) If the flywheel is to supply energy to the car as a 15.0-hp motor would, find the length of time the car could run before the flywheel would have to be brought back up to speed.
________ h

Explanation / Answer

(a) The flywheel's rotational kinetic energy is equal to 1/2 I2, where I is the flywheel's rotational moment of inertia, and is its angular velocity in rad/s. For a disk, the moment of inertia is 1/2mr2, so the kinetic energy is (1/2)(1/2)(400)(12)(5000*2/60)2 = 27.4 MJ.

(b) The time the flywheel can supply energy for is equal to its kinetic energy (in joules) divided by the power (in watts). 15 hp is 15(746)= 11.2 kW, so the flywheel can operate for 27,400,000/11,200 = 2446 seconds before being respun.

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