Angular Momentum ( 4 points ) Learning Objectives: Apply concepts of rotational motion and angular momentum. A kid of mass m = 45 kg is sitting on the edge of a merry-go-round of M = 120 kg and a radius of R = 1.8 m. It applies a force of 100 N for a time of 1.5 s in tangential direction and sets the merry-go- round into motion. (Assume that the merry-go-round is a disc rotating around a vertical axis without friction with moment of inertia of the disc of I = 1/2 MR2) a) What is the angular velocity and period of the merry-go-round after the force was applied? b) Next, the kid starts to move towards the center of the rotating merry-go-round. What is the angular velocity of the merry-go-round when the kid is 0.30 m from the center? R m kid M discAngular Momentum & Collision ( 4 points ) Learning Objectives: Apply concepts of collisions and angular momentum to describe a collision followed by rotation. A thin rod of length L = 1.00 m and mass M = 2.80 kg can turn around its upper end in a vertical plane. It is initially at rest in a vertical position. A bullet of mass m = 10.0 g is shot with velocity v = 310 m/s into the lower end of the rod where it remains embedded in the rod which starts to rotate. a) What is the angular velocity of the bullet/rod system directly after the impact? b) What is the maximum height the lower end of the rod will reach compared to its initial position? [ assume a moment of inertia of the rotation of the stick around one end of 1 = 1/3 M L2 ] M, L m, vGravitational Potential Energy ( 4 points ) Learning Objectives: Practice general calculations for gravitational potential energy using variables only. a) A satellite of mass m is in a circular orbit around Earth. When it has a total energy (kinetic + potential) of Eo - what is its potential energy? Calculate in general with variables only. b) If g is the acceleration on Earth surface - what is the gain in potential energy of an object of mass m raised from the surface of Earth to a height above Earth surface equal to the radius R of Earth? Calculate with variables only. Give the result in terms of g, and compare the result to using simply "m g h" for potential energy.Gravitation and orbit ( 4 points ) Learning Objectives: Apply laws for gravitational forces and potential energies and calculate orbits. A 25 kg satellite has a circular orbit with a period of 2.4 h and a radius of 8.0 .105 m around a planet of unknown mass. a) If the magnitude of the gravitational acceleration on the surface of the planet is 8.0 m/s2 , what is the radius of the planet? b) You want to move the satellite in an orbit 500 km higher than the original orbit. What is the energy you need for that