An initially installed flywheel can store 10⁶ J of kinetic energy when rotating at 300 rad/s.It is replaced by another flywheel of the same size but made of a lighter and stronger material.If its mass is half that of the original and it is now capable of achieving a rotational speed of 600 rad/s,what maximum energy can be stored? A)40 x 10⁵ J B)20 x 10⁵ J C)10 x 10⁵J D)5.0 x 10⁵ J

Question

Quizplus · Accepted Answer

The kinetic energy of a flywheel is given by the equation KE = 1/2 I ω^2, where I is the moment of inertia and ω is the angular velocity. Since the size of the flywheel is the same, we can assume that the moment of inertia is also the same. The initial kinetic energy of the flywheel is KE1 = 10⁶ J at an angular velocity of ω1 = 300 rad/s. The final kinetic energy of the new flywheel is KE2 = 1/2 (1/2m) ω2^2, where m is the mass of the new flywheel. Since the mass is half of the original, m/2 in the equation. Substituting the values, we get KE2 = 1/2 (1/2m) ω2^2 = 1/2 (1/2)(1/2m) (600)^2 = 5/8 m (600)^2 J. Therefore, the maximum energy that can be stored in the new flywheel is 5/8 times that of the initial flywheel. KE2 = 5/8 KE1 = 5/8 (10⁶ J) = 20 x 10⁵ J. Hence the answer is B) 20 x 10⁵ J.

An Initially Installed Flywheel Can Store 106 J of Kinetic

An Initially Installed Flywheel Can Store 10⁶ J of Kinetic