4. Two identical disks (same mass and radius) have a common axis. Initially one of the disks is spinning with a constant angular velocity. When the two disks are brought into contact, they stick together. Which of the following statements is true? (a) The total kinetic energy and the total angular momentum are unchanged from their initial values. (b) Both the total kinetic energy and the total angular momentum are reduced to half of their original values. (c) The total angular momentum is unchanged, but the total kinetic energy is reduced to half its original value. (d) The total angular momentum is reduced to one-half of its original value, but the total kinetic energy is unchanged. (e) The total angular momentum is unchanged, but the total kinetic energy is reduced to one-quarter of its original value.

A 1.10-kg particle moves in the xy plane with a velocity of Need Help? Read It = (3.70 1-3.70 ĵ) m/s. Determine the angular momentum of the particle about the origin when its position vector is = (1.50 î+ 2.20 ĵ) m. k) kg - m²/s Watch It

1. A circular object of radius R starts from rest and rolls down an incline of M, I height H without slipping. The object has a mass M, a moment of inertia / and a radius R. We go through the steps in finding the speed of the object at the bottom of the incline below, a. What is the total mechanical energy of the object at the top of the incline? Write your answer in terms of I, M, R, H and/or g. b. What is the total mechanical energy at the bottom of the incline in terms of the speed v and the givens? Use the relation v = wR to eliminate the angular speed from your expression. Check that your expression has the correct dimensions. Your final expression should only contain v, I, M, R and/or g. When an object rolls without slipping, the point in contact with the ground is at rest. Therefore, the friction the mechanical energy C. force has displacer work, conserved. Use conservation of mechanical energy to find the speed v of the object at the bottom of the hill in terms of I, R, M,H…

5) A disk of mass m = 75.0 g and radius r = 4.20 cm glides across an air table at a speed v = 1.5 m/s. It makes a glancing collision with a hoop of radius R = 5.80 cm and mass M = 130 g (initially at rest) such that their rims just touch. Because their rims are coated with instant-acting glue, the two objects stick together and rotate after the collision. a)  What is the angular momentum of the system relative to the center of mass? b)  What is the angular speed about the center of mass?

3. Two astronauts, each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speed v. Treating the astronauts as particles, calculate a) the magnitude of the angular momentum of the two-astronaut system b) the rotational energy of the system c) By pulling on the rope, one of the astronauts shortens the distance between them to d/2. What is the new angular momentum of the system? d) What are the astronauts' new speeds? e) What is the new rotational energy of the system? Where did the extra energy come from?

A marching band is performing a routine in which all players form a line that rotates about the center player C. The players complete one full 360 degrees rotation in one minute and are always in a line. Of players A and B, which player has the greater linear speed v and which player has the greater angular speed w A. Player A has a greater linear speed v, but they have the same angular speed w. B.Player B has a greater angular speed w, but they have the same linear speed v. C.Player A has a greater angular speed w, but they have the same linear speed v. D.Player B has a greater linear speed v, but they have the same angular speed w

Please answer question 8

A thin 155 g disk with a diameter of 8.50 cm rotates about an axis through its center with 0.260 J of kinetic energy. What is the speed (in m/s) of a point on the rim?

2. Assume Earth is approximately a uniform, solid sphere that has a mass of 5.98 x 1024 kg and a radius of 6.38 x 106 m. Calculate (a) angular speed, (b) the moment of inertia (treated as a sphere), (c) the rotational kinetic energy of Earth and (d) the angular momentum L as it spins on its central axis once each day (w= 1 rev/day). (a) w = (b) I = (c) KErot =

Two astronauts, each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, moving in circles around the point halfway between them at speed v. c) By pulling on the rope, the astronauts shorten the distance between them to d/2. What is the new angular momentum of the system?d) What are their new speeds?e) What is the new rotational energy of the system?f) How much work is done by the astronauts in shortening the rope?