Marie and Maria each send a spinning uniform disc towards th…

Marie and Maria each send a spinning uniform disc towards the center of an axle. Marie’s disk has a mass of 0.5 kg with a radius of 15 cm and is spinning about the axle at a rate of 120 rpm. Maria’s disk also has a mass of 0.5 kg, but a radius of 20 cm, and it spins in the same direction as Marie’s at a rate of 150 rpm. The two discs then collide and stick together. What is their final rotational speed in rad/s?

The restoring force a bow provides to an arrow as it is pull…

The restoring force a bow provides to an arrow as it is pulled back can be modeled as a spring force. The archer Gila “nocks” an 18-g arrow by pulling it back a distance of 45 cm. Gila fires the arrow horizontally from a small cliff with a height of 12 m, and when the arrow reaches the bottom, it has a speed of 63 m/s. What is the effective spring constant of the bow as Gila nocks the arrow?