A wheel of moment of inertia 2 Kg m² is rotating about an axis passing through centre and perpendicular to its plane at a speed 60 rad/s. Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is A) 24 Kg m?/s C) 72 Kg m?/s B) 48 Kg m²/s D) 96 Kg m²/s
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- i need the answer quicklyA 87.5 kg horizontal circular platform rotates freely with no friction about its center at an iñitial angular velocity of 1.53 rad/s. A monkey drops a 8.75 kg bunch of bananas vertically onto the platform. They hit the platform at of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 21.1 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 1.55 m. angular velocity: rad/sA 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)If initial angular velocity is 0 deg/s (w;), which of the following situations would result in the greatest final angular velocity (w;)? (T = torque applied; Dt-time that torque is applied; I = moment of inertia) OT-50 Nm t = 2s 1 = 1 kgm^2 T= 50 Nm t = 4s 1 = 2 kgm^2 OT-100 Nm ?t=1s 1 = 2 kgm^2 OT-100 Nm ?t=2s 1 = 1 kgm^2 - 2 | M 16 46 6 Y & 7 18 U * 8 hp fg ( 9 ho ▶11 O fm P 112 74° +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?5) In ice figure skating, a couple execute a “top” (see picture). The centre of mass of the woman (58 kg) is situated 1.3 m from the axis of rotation which is vertical and passes through the centre of mass of the man (85 kg). They are spinning at a constant angular velocity equal to ?? rad/s and the man and woman have moments of inertia, about their own centres of mass, equal to 1.6 and 2.5 kg.m2 respectively. Then the woman grabs the neck of the man. At this point, her moment of inertia decreases to 1.4 kg.m2 and her body centre of gravity is 0.9 m from the axis of rotation. Determine the new angular velocity. Hints: This is a conservation of angular momentum problem, and needs the parallel axis theorem to determine moments of inertia about the axis of rotation. The skaters are moving as one body with one angular velocity, but they each have their own moments of inertia given relative to their own CoMs. For the man, that’s fine…the axis they’re rotating about passes through his CoM,…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?). [
- F1 = 5 kN F2 = 13 kN 0- 45° 60° F3 = 4 kN A 4 m 8m F4 = 22 kN E lkJa= 30° F5 = 4 kN 1] What is the resultant moment of the five forces acting on the rod about point B? a) 40.5 kN.m b) 49.5 kN.m e) 39.1 kN.m d) 18.5 kN.m e) 9.1 kN.m ) 21.1 kN.m 2] What is the resultant moment of the five forces acting on the rod about point E? a) - 22.8 kN.m b) - 2.8 kN.m c) - 18.9 kN.m d) - 8.1 kN.m e) - 12.7 kN.m )- 7.5 kN.m 3] What is the moment of the force F1 about point D? a) - 27.8 kN.m b) - 12.8 kN.m c) - 38.9 kN.m d) - 19.1 kN.m e) - 32.7 kN.m )- 29.2 kN.m 4] What is the moment of the force F2 about point E? a) 77.5 kN.m b) 55.5 kN.m c) 14.2 kN.m d) 32.5 kN.m e) 7.1 kN.m ) 84.1 kN.m Activate Windows 5] What is the moment of the force F5 about point B? Go to Settings to activate W e) - 29.7 kN.m a) - 39.8 kN.m b) - 18.8 kN.m c) - 12.8 kN.m d) - 4.1 kN.m )- 25.9 kN.n WE5) 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?A hollow, iron sphere has a radius R = 0.8 m and mass M = 8 kg. IT rotates at a constant àngular speed of 1.2 rad/s about an axis veritcal and passing through-its center. What is its angular momentum? %3D