A turntable has a radius of R = 1.3 m and a moment of inertia of 2.0 kg · m^2. The turntable is rotating with an angular velocity of w = 1.4 rad/s about a vertical axis though its center on frictionless bearings. A small ball with mass m = 0.50 kg is projected horizontally toward the turntable axis with a velocity of 3.7 m/s. The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure). Find the percent of the kinetic energy of the system that is lost during the capture of the ball.