While spinning down from 500.0 rpm to rest, a solid uniform flywheel does 5.1 kJ of work. If the radius of the disk is 1.2 m, what is its mass?
A) 5.2 kg
B) 4.4 kg
C) 6.0 kg
D) 6.8 kg

Question

Quizplus · Accepted Answer

The work done by the flywheel is equal to its change in kinetic energy. The initial kinetic energy of the flywheel is:$$K_i = \frac{1}{2}I\omega_i^2$$where I is the moment of inertia of the flywheel and \omega_i is its initial angular velocity. The final kinetic energy of the flywheel is zero. Therefore, the work done by the flywheel is:$$W = K_f - K_i = -\frac{1}{2}I\omega_i^2$$The moment of inertia of a solid uniform flywheel is:$$I = \frac{1}{2}MR^2$$where M is the mass of the flywheel and R is its radius. Substituting this into the equation for the work done by the flywheel, we get:$$W = -\frac{1}{4}MR^2\omega_i^2$$Solving for M, we get:$$M = -\frac{4W}{R^2\omega_i^2}$$Substituting the given values, we get:$$M = -\frac{4(5.1 	ext{ kJ})}{(1.2 	ext{ m})^2(500.0 	ext{ rpm})^2}$$$$M = 5.2 	ext{ kg}$$Therefore, the mass of the flywheel is 5.2 kg.

While Spinning Down from 500