A hollow, iron sphere has a radius R = 0.5 m and mass M = 11 kg. IT rotates at a constant angular speed of 1.0 rad/s about an axis veritcal and passing through its center. What is its angular momentum? %3D
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constant angular speed of 1.0 rad/s about an axis veritcal and passing through its
center. What is its angular momentum?
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- Axis 1 CML A large circular platform is supported on frictionless bearings and is at rest. A 68 kg runner also at rest on the platform begins running in a counter-clockwise 4 meter circular path and the platform rotates in the opposite direction. The observed angular velocity of the platform is 0.59 rad/s. Determine the runner's (a) angular velocity in rad/s m/s, (b) linear velocity with respect to the observer in m/s and (c) linear velocity with respect to the moving platform. The mass moment of inertia of the platform is 3046 kg-m^2. Express algebraic solution of (b) in terms of m, R, omega and lo. m 68 R 4 00 lo 0.59 3046A 0.02 kg mass red object (bead) is moving at a speed of 10.0 m/s when it sticks to the edge of a uniform solid cylinder. The cylinder is free to rotate about its axis through its center and has a mass of 0.5 kg , a radius of 0.25 m and is initially at rest. I = 1/2MR2^2 a) What is the angular velocity of the system after the collision? b) How much kinetic energy is lost in the collision? c) If the angular position of the Cylinder varies as θ(t)=3.2t-t^2 find the centripetal acceleration of the red object (bead). d) A cord is now wrapped around the cylinder. Use the work energy theorem to find the angular velocity of the cylinder after 5.0m of cord have been removed by a 40N Force. e) If the 40N force on the cord is replaced by a 40-N weight, what is the angular velocity of the cylinder after 5.0m of cord has unwound?A ficle is located at position r=3î+7g+4€ par %3D 3. with respect to the origin. It has linear momentum D= -î +9Te ka ms! what is its angular momentum?
- A 95.5 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.75 rad/s. A monkey drops a 8.65 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 22.1 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 1.79 m. angular velocity: rad/s about us careers privacy policy terms of use contact us helpA 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 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.
- Ex. 6: The moment of inertia of the earth about its axis of rotation is 9.83 x 107 kg-m2 and if its angular velocity is 7.3 x 10-5 rad/s. Calculate (1) Kinetic energy of rotation and (2) Radius of gyration. (Given : mass of the earth 6 x 1024 g) %3DA 10 kg particle moves in the xy plane with a velocity of v = (3.2 î-6.1 ) m/s. Determine the angular momentum of the particle when its position vector is 7 =(3 i +2.2 j) m. %3D O a:(-253.4k) kg.m2/s Ob:(+253.4 k) kg.m²/s OC(-25.34 k) kg.m²/s d(+25.34 k) kg.m²/sA 1.70-kg particle moves in the xy plane with a velocity of = (4.10 1-4.00 j) m/s. Determine the angular momentum of the particle about the origin when its position vector is F (1.50 +2.20 j) m. + j+ k) kg - m²/s
- PlzA clock hangs on a wall. a) What is the direction of the average angular velocity of the seconds hand? b) What is the magnitude of the average angular velocity of the seconds hand?Modern wind turbines generate electricity from wind power. The large, massive blades have a large moment of inertia and carry a great amount of angular momentum when rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 12 rpm. a)Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared. b)Enter an expression for the angular momentum of the wind turbine, in terms of the defined quantities. c)Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.