A 2.4-kg 13-cm-radius cylinder, initially at rest, is free to rotate about the axis of the cylinder. A rope of negligible mass is wrapped around it and pulled with a force of 20 N. (a) Find the magnitude of the torque exerted by the rope. N. m (b) Find the angular acceleration of the cylinder. rad/s2 (c) Find the angular velocity of the cylinder at t = 1.90 s. rad/s
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- A playground merry-go-round of radius R = 1.80 m has a moment of inertia I = 255 kg. m² and is rotating at 12.0 rev/min about a frictionless vertical axle. Facing the axle, a 23.0-kg child hops onto the merry-go-round and manages to sit down on the edge. What is the new angular speed of the merry-go-round? rev/minA small 700 g ball on the end of a thin, light rod is rotated in a horizontal circle of radius 2.5 m. Calculate the torque needed to keep the ball rotating at a constant angular speed if the air resistance experienced by the ball is 0.0200 N. Ignore the rods moment of inertia and air resistance. Hint: Treat the small ball as a particle.A 3.00 kg solid sphere with a radius of 15 cm is rolling without slipping along a horizontal floor. The magnitude of the velocity of the center of mass is 3.00 m/s. What is the ratio of the sphere's rotational kinetic energy to its translational kinetic energy, KErot / KEtrans? 2.
- A yo‑yo with a mass of 0.0850 kg and a rolling radius of r=1.60 cm rolls down a string with a linear acceleration of 5.20 m/s2. Calculate the tension magnitude ? in the string and the angular acceleration magnitude ? of the yo‑yo.A model airplane with mass 0.749 kg is tethered to the ground by a wire so that it flies in a horizontal circle 30.0 m in radius. The airplane engine provides a net thrust of 0.807 N perpendicular to the tethering wire. (a) Find the magnitude of the torque the net thrust produces about the center of the circle. N. m (b) Find the magnitude of the angular acceleration of the airplane. rad/s2 (c) Find the magnitude of the translational acceleration of the airplane tangent to its flight path. m/s2A motor spins a disk (Idisk = 25.5 kg*m2) with a torque of 39 N*m, and a 18 N frictional force acts on the disk at a radius of 1.4 m. Attached to the disk at a radius of 6.6 m is a 13 kg mass. What is the magnitude of the angular acceleration in rad/s2 of the system?
- A 10 kg cylindrical barrel with a radius of 0.5 m rotates about a vertical axis of rotation without displacing with an initial angular velocity of 4 rad/s. The rotational inertia of the cylindrical barrel is 0.3mr2 and rain begins to fill the barrel with water as it rotates. If the barrel accumulates 4 kg of water, calculate the new angular velocity of the barrel.An automobile engine can produce 253 Nm of torque. Calculate the angular acceleration (in rad/s2) produced if 80.2% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00 kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0 kg hoop of radius 0.330 m. The 12.1 kg axle acts like a rod that has a 2.00 cm radius. The 29.7 kg drive shaft acts like a rod that has a 3.20 cm radius. rad/s² t Additional Materials ReadingTwo forces act on a uniform disk with a radius of 2.0 cm and a mass of 20.0 g which is initially at rest. After 1.25 s the disk has an angular velocity of 250 rad/s counterclockwise. Determine the force F2 if F1 has a magnitude of 0.1 N. Write your answer to the hundredth newton.
- A circular disk with a radius of 0.38 m is subject to 2 tangentially applied forces. The disc is fixed such that it will rotate about its center. Both forces produce a torque in the same direction. F1 = 3.6 N applied at the outer edge of the disc. F2 = 4.3 N applied at a distance of 0.28 from the center of the disc. What is the net torque on the disc?A motor spins a disk (Idisk = 25.1 kg*m2) with a torque of 40 N*m, and a 18 N frictional force acts on the disk at a radius of 1.5 m. Attached to the disk at a radius of 2.6 m is a 17 kg mass. What is the magnitude of the angular acceleration in rad/s2 of the system?