A 14 lb bowling ball is thrown onto a lane with a backspin angular speed of 10 rad/s and forward velocity of 25 ft/s. After a few seconds, the ball starts rolling without slip and forward velocity of 17.2 ft/s and angular velocity of 48.6 rad/s. The ball has a mass moment of inertia of 0.0204 slugs-ft2. Determine the work done by friction on the ball from the initial time until when it starts rolling without slip.

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)