1-) A 210g , 43.0-cm-diameter turntable rotates on frictionless bearings at 68.0rpm . A 24.0g block sits at the center of the turntable. A compressed spring shoots the block radically outward along a frictionless groove in the surface of the turntable. What is the turntable's rotation angular velocity when the block reaches the outer edge?
2-) A 45kg figure skater is spinning on the toes of her skates at 0.50rev/s . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40kg , 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 71cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20-cm-diameter, 200-cm-tall cylinder. What is her new rotation frequency, in revolutions per second?