A turntable with rotational inertia I is spinning on a frictionless axis at an initial angular speed of ωo. A funnel is positioned above the turntable and drops syrup in a circle onto the turntable at a radius of R. If the funnel drops the syrup at a rate of S kg/s, what is the speed of the turntable as a function of time?

The man of mass m1 and the woman of mass m2 are standing on opposite ends of the platform of mass m0 which moves with negligible friction and is initially at rest with s = 0. the man and woman begin to approach each other. derive an expression for the displacement s of the platform when the two meet in terms of the displacement x1 of the man relative to the platform.