Solve the following questions with step-by-step work shown:

1.

A particle of mass 3.5 kg has position vector " = (4 8 - 4 p) mat a particular instant of time when its velocity is D = (3.0 #) m/'s with respect to the origin. a, What is the angular momentum of the particle? kg m /s in the direction b. If a force F = 5.07 N acts on the particle at this instant, what is the torque about the origin? T N m in the direction Add WorkUse G = 6.674 x 10 1 N m' / kg to answer below questions. a, Evaluate the gravitational potential energy between two 5.00-kg spherical steel balls separated by a center-to center distance of 13.6 cm. U = x 10 b. Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast will they be traveling upon impact. Each sphere has a radius of 5.1 cm. * 10 5 m/s Add WorkA satellite of unknown mass Is 820,000 meters above Earth's surface. Earth has a radius of 6,371,000 meters and a mass of 5.972:10- kg. If the satellite is moving in a constant, circular orbit, what must its acceleration be? m/s2 What is the speed of the satellite? m/s How long does it take to complete an orbit? T Add WorkA bullet of mass 6.2 grams is traveling at 385 m/s when it strikes a cylinder (edge on) that is at rest. The bullet becomes stuck In the edge of the cylinder, which rotates as a result. The cylinder has a mass of 19.7 g and a radius of 0.44 meters. What is the angular momentum of the bullet before impact? kg m'/s What is the angular momentum of the bullet. cylinder system after impact? kg m'/s What is the angular velocity of the bullet-cylinder system after Impact? rad/s Add Work