A large wind turbine has I= .45 mr². The mass of the turning hub and blades is 3800 kg with a radius of 40. m. It is rotating at exactly +4 radians/s. Wind provides a positive torque of 1000 Nm, while the generator resists the rotation with a force of 14000 N exerted .085 m from the center. a.) What is the direction of the net torque net torque?(positive or negative) b.) What is the magnitude of the net torque? Nm c.)What is the moment of angular inertia of the turbine? million kgm² d.) What is the angular acceleration of the turbine?-.0000 rad/s? e.) How fast is the turbine rotating after 12000 s under these conditions? rad/s

A circular disk with a radius of 0.37 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 = 4.7 N applied at the outer edge of the disc. F2 = 3.2 N applied at a distance of 0.3 from the center of the disc. What is the net torque on the disc?

A circular disk with a radius of 0.42 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 = 4.4 N applied at the outer edge of the disc. F2 = 3 N applied at a distance of 0.2 from the center of the disc. What is the net torque on the disc?

A toy Ferris wheel that is at rest has a radius of 20.0 cm. A perpendicular force of 1.5 N is applied to the outer most part of the Ferris wheel. The toy Ferris when has a rotational inertia of 0.050 kg m2 . a) What is net Torque applied to the Ferris wheel? b) What is the angular acceleration of the Ferris wheel? k) If the Ferris wheel maintains this angular acceleration for 3.0 seconds, what will its final angular velocity be? d) What will be its rotational Kinetic Energy after 3.0 seconds?

A 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/s²

A student holds a bike wheel and starts it spinning with an initial angular speed of 9.0 rotations per second. The wheel is subject to some friction, so it gradually slows down. In the 10.0 s period following the inital spin, the bike wheel undergoes 77.5 complete rotations. Assuming the frictional torque remains constant, how much more time At, will it take the bike wheel to come to a complete stop? Ats = %3D S

T m A 25.0 kg mass is hung from a rope that is passed over a pulley and held by a man standing on a ramp. The pulley can be treated as a solid disk with a mass of 10.0 kg that has a radius of 0.400 m. The man pulls the rope so that the pulley rotates from rest through an angular displacement of 15.0 rad in 2.00s. A. What is the angular acceleration of the disk? B. What is the tension of the rope as it pulls up on the box? C. What is the force applied by the man on the rope as he pulls the box upward?

a.) A tension force, T, of magnitude 5.0 N is applied to the end of a bar at a distance r = 1.5 m from the axis of rotation O (represented by the black dot). The angle between the force and the distance vector, θ=25o. Calculate the magnitude and direction of the torque vector.   b.) In the previous problem, let’s make some changes.  The bar is now a different length and reoriented within 3-D space such that the r is a vector that has components (3,2,0) in the xyz coordinate frame, and F is a vector with components (4,5,0). What is the torque exerted on the rigid body about a pivot located at the origin? Express your answer in i, j, k, components.  Assume all distances are represented in meters and forces in newtons.

A 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

A solid 0.6150 kg ball rolls without slipping down a track toward a vertical loop of radius ?=0.7350 m. What minimum translational speed ?minvmin must the ball have when it is a height H=1.111 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller than the loop radius ?R. Use g=9.810 m/s^2 for the acceleration due to gravity.