A uniform solid disk with a mass of 41.3 kg and a radius of 0.296 m is free to rotate about a frictionless axle. Forces of 90.0 and 125 N are applied to the disk, as the figure illustrates. Taking the clockwise direction to be the negative direction, what is (a) the net torque produced by the two forces and (b) the angular acceleration of the disk? (a) Number i (b) Number i Units Units 90° 90° 125 N 90.0 N
Q: 90° 125 N 90 90.0 N
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- Problem 2: When a 3.75-kg fan, having blades 22.5 cm long, is turned off, its angular speed decreases uniformly from 11.0 rad/s to 7.20 rad/s in 6.00 s. (a) What is the magnitude of the angular acceleration of the fan? (2 pts) (b) Through what angle (in degrees) does it turn while it is slowing down during the 6.00 s? (1 pt) (c) If its angular acceleration does not change, how long after it is turned off does it take the fan to stop.A solid cylinder with a mass of 300.0g and a radius of 20.0cm is rotating at 50.0 rad/s. A metal hoop of mass 200.0g and radius 10.0cm, initially not rotating, is dropped onto the rotating solid cylinder so that their rotational axes align. Determine the angular speed of the 2 objects as they rotate together. Report your answer in radians per second, but only enter in the numerical value.Two disks are free to rotate about an axis through their center. The inner disk has a radius a = 20 cm and a 60 N force is applied tangent to the rim as shown. The outer disk has radius b = 40 cm and a force of magnitude F is applied tangent to its rim. What value of F is required to give zero net torque about the center?
- The fly wheel is an important mechanical element in machines that is used to increase the moment of inertia of the machine and store rotational kinetic energy. A fly wheel of an engine starts rotating about a fixed axis from rest to 102 rad/s in 6.3 seconds. The wheel has a radius of 0.5 meters and mass of 88 kg. Calculate the net torque acting on the fly wheel during the time interval t = 0; 6.3 s measured in Nm (Enter the number only).A dragster starts from rest and accelerates down a track. Each tire has a radius of 0.320 m and rolls without slipping. At a distance of 418 m, the angular speed of the wheels is 255 rad/s. Determine (a) the linear speed of the dragster and (b) the magnitude of the angular acceleration of its wheels. (a) v = (b) a= i iA disk, initially rotating at 113 rad/s, is slowed down with a constant angular acceleration of magnitude 3.04 rad/s2. (a) How much time does the disk take to stop? (b) Through what angle (rad) does the disk rotate during that time? (a) Number i Units (b) Number i Units
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- A disk, initially rotating at 101 rad/s, is slowed down with a constant angular acceleration of magnitude 3.90 rad/s?. (a) How much time does the disk take to stop? (b) Through what angle (rad) does the disk rotate during that time? (a) Number Units (b) Number i UnitsA counterweight of mass m = 3.60 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 7.00 cm and mass M = 1.50 kg. The spokes have negligible mass. M m (a) What is the net torque on the system about the axle of the pulley? magnitude 2.058 x N.m direction to the right along the axis of rotation (b) When the counterweight has a speed v, the pulley has an angular speed = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. (0.357 kg. m)v (c) Find the magnitude of the acceleration of the counterweight. 5.76 x m/s²A counterweight of mass m = 3.60 kg is attached to a light cord that is wound around a pulley as shown in the figure below. The pulley is a thin hoop of radius R = 7.00 cm and mass M = 3.00 kg. The spokes have negligible mass. (a) What is the net torque on the system about the axle of the pulley? V N.m to the right along the axis of rotation v magnitude 2.4695 direction (b) When the counterweight has a speed v, the pulley has an angular speed w = v/R. Determine the magnitude of the total angular momentum of the system about the axle of the pulley. (3.705 Note that your numerical answer is multiplied by the symbol v in the answer box. kg • m)v (c) Using your result from (b) and 7 = L/dt, calculate the acceleration of the counterweight. (Enter the magnitude of the acceleration.) 6.925 The expression for the angular momentum in part (b) has a factor of v. How do you determine dL/dt, from this expression? m/s2