nt C 6. Solid sphere CM = MR² 5 2 J R с 2R a) Find the moment of inertia of solid sphere spinning around the axis of c. b) Define and draw the direction of angular velocity, torque, and angular momentum.
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- 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 200kg disk with a radius of 4.0m is rotating clockwise about the +y axis. A 50kg person is sitting 2.5m from the rotational axis. a) What is the total moment of inertia of the disk and person together? b) What is the initial angular momentum Li of the system? c) A constant 30.0N force is applied to the edge of the disk with an angle of 60° with respect to the moment arm. (+y out of page in top down view) What is the torque on the system? d) What is the final angular momentum if the torque is applied for 2s?A bowler throws a bowling ball of radius R = 11 cm along a lane. The ball (the figure) slides on the lane with initial speed vcom.O friction between the ball and the lane is 0.29. The kinetic frictional force 7k acting on the ball causes a linear acceleration of the ball while producing a torque that causes an angular acceleration of = 8.4 m/s and initial angular speed wo 0. The coefficient of kinetic the ball. When speed vcom has decreased enough and angular speed p has increased enough, the ball stops sliding and then rolls smoothly. During the sliding, what are the ball's (a) linear acceleration and (b) angular acceleration? (c) How long does the ball slide? (d) How far does the ball slide? (e) What is the linear speed of the ball when smooth rolling begins? Note that the clockwise direction is taken as negative. Vcotm (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
- In orbit mechanics, the angular momentum is also an important quantity governing the satellite's motion. Assume planar motion, a satellite is orbiting around Earth center within a fixed plane. Thus it's motion is completely described by the distance r and the angle (relative to some reference direction). êo 0 (center of Earth) êr PO.. P (satellite) satellite's trajectory Obtain the satellite's angular momentum with respect to Earth center. For spacecrafts, the angular momentum (h) is h = Fx, it is independent of mass. What is the magnitude of h?A solid metal disk with moment of inertia I, radius R, and mass m1 can rotate freely about a frictionless axis passing through its center. A light string is wrapped around the disk and connects to a hanging mass m2. The hanging mass is released from rest at a distance d above the ground and accelerates downward with acceleration awhile the disk rotates through an angle q. a) Find an expression for the angular accelerationaof the diskin terms of m2, I, R, and any necessary constants. b) Find an expression for the time it takes for the hanging mass to reach the ground. Write your answer in terms of q, a, and any necessary constants. c) Find an expression for the angular velocity of the disk just before the hanging mass hits the ground. Write your answer in terms of q, a, and any necessary constants.Modem 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 rotatingA wind turbine has a total of 3 bladesEach blade has a mass of m 5500 kg distributed uniformly along its length and extends a distance r = 49m from the center of rotationThe turbine rotates with a frequency of f= 15 rpm. Part a: enter expression for the total moment of inertia of the wind turbine about its a is of rotation in terms of the define quantites Part b calcukate the total moment of inertia of the wijd turbine about its axis in units of kilogram meter square Part c enter an expression for the expression for the angular momentum of the wind turbine in terms of the defined quantities Part d : calculate the angular momentum of rhe wind turnine in units if kilogram meters squared per second
- A disk of radius R, mass M, and moment of inertia I = (1/2)MR- rolls without slipping down an incline and onto a horizontal table. The disk then continues to the right and goes up a frictionless ramp. The disk starts at rest at a height h above the table, as shown . What is the speed of the center of mass of the disk when it reaches the bottom of the ramp? O A. V1/2gh OB. V5/3gh OC. 4/3 gh OD. 6/7gh O E. None of the above2. A thin square plate of mass m rotates on a smooth surface with an angular velocity of æn about its mass center. The hook then strikes the peg at P and the plate starts to rotate about point P with no rebound. What is the plate's angular velocity after impact, and the speed vg of the mass center of the plate?TWo metal disks,one with radius R, = 2.50 cm and mass M, = 0.90 kg and the Other with radius Rz =5.00 cm and mass M2= 2.00 kg , are welded together and mounted on frictionless axis through their common center. A.) What is the total moment of inertia of the two disks. B.)A light string is wrapped around the edge of the smaller disk, and a 1.50 kg block is suspended from the free end of the string. If the block is released from rest at a distance of 2.00 m above the floor, what is its speed just before it Strikes the floor. R2 1.50 kg