An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pull in closer to the body, in which of the following ways are the angular momentum and kinetic energy of the skater affected?

Two astronauts (figure), each having a mass of 70.0 kg, are connected by a d = 11.0-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.30 m/s. CM X (a) Treating the astronauts as particles, calculate the magnitude of the angular momentum of the two-astronaut system. kg-m²/s (b) Calculate the rotational energy of the system. (c) By pulling on the rope, one astronaut shortens the distance between them to 5.00 m. What is the new angular momentum of the system? kg-m²/s (d) What are the astronauts' new speeds? m/s (e) What is the new rotational energy of the system? (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? kJ

After all the metal has unwound from the roller, the student measures the radius R and the angular speed wo of the roller to be 25 cm and 20 rad/s respectively. Observed from the side, the roller rotates counterclockwise, as shown. A piece of clay of mass m strikes the very bottom edge of the roller with a horizontal velocity v = 4.0 m/s. The clay sticks to and rotates with the roller. The clay-roller system then rotates with a final angular velocity wi. (f) Is wi greater than, less than, or equal to wo? Justify your answer.

Consider the father pushing a playground merry-go-round. He exerts a force of 250 N at the edge of the 50.0-kg merry-go-round, which has a 1.50-m radius. Calculate the angular acceleration produced (a) when no one is on the merry-go-round and (b) when an 18.0-kg child sits 1.25 m away from the center. Consider the merry-go- round itself to be a uniform disk with negligible friction.

A point particle travels in a straight line at constant speed, and the closest distance it comes to the origin of coordinates is a distance l. With respect to this origin, does the particle have nonzero angular momentum? As the particle moves along its straight-line path, does its angular momentum with respect to the origin change?

Can you please help me answer the last three parts of this same problem.  Question 4: What is the skater's angular momentum?please answer in kg m^2 /s Question 5: The skater pulls his arms in to his chest and now he can be approximted as just a cylinder. What is his new moment of inertia? Please answer in kg m^2 Question 6: How fast is he spinning now that his arms are pulled in? Assume no external torque acts on him as he spins. Please answer in rad/s

6. For vectors B = -î – 4ĵ and Å = -31 – 2j, calculate: a. Ā +B and its magnitude and direction angle b. A-B and its magnitude and direction angle.

A 150-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. (a) What constant force must be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.500 rev/s in 2.00 s? (b) What is the angular momentum of the disk during this time?

A 89.9 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.61 rad/s. A monkey drops a 9.19 kg bunch of bananas vertically onto the platform. They hit the platform at 45 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 20.7 kg, drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.57 m.

Two astronauts each having a mass of 75kg are connected by a 10m rope of negligible mass. They are isolated in space, orbiting thier center of mass at speeds of 5 m/s. a) Treating the astronauts as particles, calculate the magnitude of the angular momentum and the rotational energy of the system b) By pulling on the rope, one of the astronauts shortens the distance between them to 5m. What is the new angular momentum of the system?