-F A rod with a mass of m= 15 kg and length 1 = 9 m hangs at rest when the force F= 264 N is applied. Find the angular velocity of the rod when it has rotated 90° clockwise.
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- Sub Parts (D,E,F)A cockroach of mass m lies on the rim of a uniform disk of mass 8.00m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.320 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then iş the angular velocity of the cockroach-disk system? rad/s (b) What is the ratio K/Ko of the new kinetic energy of the system to its initial kinetic energy? (c) What accounts for the change in the kinetic energy? (Select all that apply.) O cockroach does negative work on the disk O gravity O centripetal force O friction O centrifugal force O cockroach does positive work on the diskTwo astronauts, each having a mass of 75.5 kg, are connected by a 10.0 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 4.90 m/s. Treating the astronauts as particles, calculate each of the following. Center of gravity (a) the magnitude of the angular momentum of the system kg-m²/s (b) the rotational energy of the system KJ By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? kg-m²/s (d) What are their new speeds? m/s (e) What is the new rotational energy of the system? KJ (f) How much work is done by the astronauts in shortening the rope? kJ
- A cord is wrapped around the rim of a wheel 0.225 m in radius, and a steady pull of 41.5 N is exerted on the cord. The wheel is mounted on frictionless bearings on a horizontal shaft through its center. The moment of inertia of the wheel about this shaft is 5.50 kg m² 世 ProvThe uniform disk of mass m is rotating with an angular velocity of v0 when it is placed on the floor. Determine the initial angular acceleration of the disk and the acceleration of its mass center. The coefficient of kinetic friction between the disk and the floor is μk.A mountain biker takes a jump in a race and goes airborne. The mountain bike is traveling at 12.5 m/s before it goes airborne. If the mass of the front wheel on the bike is 950 g and has radius 30 cm, what is the angular momentum (in kg · m/s) of the spinning wheel about its axis in the air the moment the bike leaves the ground? (Assume the wheel can be approximated by a hoop rotating about its center of mass that rolls without slipping before the jump. Enter the magnitude.) kg · m2/s
- 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 uniform 3.7-kg cylinder can rotate about an axis through its center at O. The forces applied are: F1 = 4.5 N, F2 = 7.1 N, F3 = 5.8 N, and F4 = 3.8 N. Also, R1 = 11.1 cm and R3 = 6.2 cm. Find the magnitude and direction (+: counterclockwise; -: clockwise) of the angular acceleration of the cylinder.A cockroach of mass m lies on the rim of a uniform disk of mass 3.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.434 rad/s. Then the cockroach walks halfway to the center of the disk.(a) What then is the angular velocity of the cockroach-disk system?(b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?
- Someone frequently throws a tennis ball for their dog to chase.Throughout the throwing motion, the angular velocity of their arm is 6.7radians/s, and the radius of rotation of the ball is 63.0 cm.One day they decide to test out a ball-throwing tool which effectivelyextends the radius of rotation by an extra 36 cm. Assuming all othervariables are equal, how much faster (in m/s) can they throw the ballwhen they use the launcher compared to when they don't?Express your answer to 2 decimals, and don't include units+. Please type answer not write by hendA uniform 3.7-kg cylinder can rotate about an axis through its center at O. The forces applied are: F1 = 4.5 N, F2 = 7.1 N, F3 = 5.8 N, and F4 = 3.8 N. Also, R1 = 11.1 cm and R3 = 6.2 cm. Find the magnitude and direction (+: counterclockwise; -: clockwise) of the angular acceleration of the cylinder.A uniform disk of radius R is free to rotate about its central axis. A mass m is hung vertically from the disk at a distance 2/5 R from the axis. R 2R/5 m What is the magnitude of the force F (the solid-lined arrow in the figure) which must be applied to prevent the disk from rotating? Omg O 3mg/5 O2mg/5 O 5mg/2