A rod 2-meter long rod is initially at rest and is fixed on its right side, which acts as its axis of rotation. A 200 N force acts on the rod 0.5 meters away from the axis of rotation downward and a 100 N force acts on the rod 1.5 meters away from the axis of rotation. Calculate the angular momentum of the rod after 2 seconds have past.
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- 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.A disk initially at rest is fixed to a vertical axis of rotation and a 40 kg child is standing on the disk initially at rest 0.5 meters away from the axis of rotation. The rotational inertia of the disk is 50 kgm2. The boy pushes and jumps off the disk and the disk begins to rotate at 0.5 rad/s. Calculate the velocity of the child as they push off the disk. (The rotational inertia of the boy is mr2)A disk initially at rest is fixed to a vertical axis of rotation and a 40 kg child is standing on the disk initially at rest 0.5 meters away from the axis of rotation. The rotational inertia of the disk is 50 kgm2. The boy pushes and jumps off the disk and the disk begins to rotate at 0.5 rad/s. Calculate the velocity of the child as they push off the disk. (The rotational inertia of the boy is mr2)
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- A disk initially at rest is fixed to a vertical axis of rotation and a 40 kg child is standing on the disk initially at rest 0.5 meters away from the axis of rotation. The rotational inertia of the disk is 50 kgm2. The boy pushes and jumps off the disk and the disk begins to rotate at 0.5 rad/s. Calculate the velocity of the child as they push off the disk. (The rotational inertia of the boy is mr2)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?A rod 2-meter long rod is initially at rest and is fixed on its right side, which acts as its axis of rotation. A 200 N force acts on the rod 0.5 meters away from the axis of rotation downward and a 100 N force acts on the rod 1.5 meters away from the axis of rotation upwards. Calculate the angular momentum of the rod after 2 seconds have past.
- Problem 5) (Conservation of angular momentum) Before A merry-go-round with a radius of 2.5 meters and mass of M = 175 kg has an angular velocity of 0.5 rev/s. A boy with a mass of m = 25 kg runs and jumps tangentially on the edge of the merry- go-round and holds on the rail. What is the final angular speed of the boy+merry-go-round? (Hint: the initial angular momentum of the kid is mass times velocity times the radius, i.e., mvr, and his final moment of inertia is mr?). [A particle is acted on by two torques about the origin: 7₁ has a magnitude of 3.7 N-m and is directed in the positive direction of the x axis, and 72 has a magnitude of 5.2 N-m and is directed in the negative direction of the y axis. In unit-vector notation, find de Idt, where is the angular momentum of the particle about the origin. Number i i ĴUnitsA disk initially at rest is fixed to a vertical axis of rotation and a 40 kg child is standing on the disk initially at rest 0.5 meters away from the axis of rotation. The rotational inertia of the disk is 50 kgm2. The boy pushes and jumps off the disk and the disk begins to rotate at 0.5 rad/s. Calculate the linear velocity of the child as they push off the disk. (The rotational inertia of the boy is mr2)