The flywheel of a gasoline engine is required to give up 500 J of kinetic energy while its angular velocity decreases from 650 rev/min to 520 rev/min. What moment of inertia is required?

Video transcript

Hello everyone. So in this problem apply wheel of a steam engine rotates at an angular speed, 70 radiance for a second. When it releases 80 jewels of kinetic energy, its angular speed drops 40 radiance for a second. What is its moment of inertia? So we have some change in kinetic energy. Recall that the change of kinetic energy is equal to one half. I delta omega swim. Omega is the only variable that is changing its problem as I is constant. So we can rearrange this equation for I to get two times delta kinetic energy over delta omega sweet and we can expand delta omega squared to get two times delta K over omega F squared minus will make an I squared final minus the initial angular velocities. And in this problem we're given both the final and the initial Where Omega is equal to 40 ratings for a second And don't make a. I. is equal to 70 readings per second. Were also given that it releases 80 jewels. So Delta K. is negative 80 jewels. So we can make these substitutions and find At the moment of Inertia is just two times negative 18 tools over Omega F, which is 40 radiance for a second squared minus 70 ladies for a second square, Which is equal to 0. kg times m. This is answer choice B. Of the sounds great