If an energy of 684 J is needed to increase the speed of a fly wheel from 180 rpm to 360 rpm , then find its moment of inertia.

Step-by-step solution

Given the initial speed, 180   rpm = 180 × 2 π 60   rad   s - 1   and final speed of the flywheel 360   rpm = 360 × 2 π 60   rad   s - 1   The energy given to the flywheel will increase the rotational kinetic energy of the flywheel, therefore, change in rotational kinetic energy will be ∆ K E = 1 2 I ∆ ω 2 = 684   J 684   J = 1 2 I ω f - ω i 2 ⇒ I = 684 × 2 360 × 2 π 60 - 180 × 2 π 60 2 =