Hoop or thin cylindrical shell Hollow cylinder Solid cylinder or disk Rectangular plate MR Long, thin rod with rotation axis thưough center Long, thin rod with rotation axis through end MI Solid sphere Thin spherical shell ku = M

A mass (M = 5.0 kg) is connected to a two pulley system. Pulley 1 has a moment of inertia, I = 0.5 kgm2, and a radius, R = 0.2 m. Pulley 2 has moment of inertia, I = 0.3 kgm2, and a radius, R = 0.15 m. The cord is spooled around pulley 2. The pulleys rotate about frictionless axles and the cord can be considered massless. (i) Determine the magnitude of the acceleration of m (ii) Determine the magnitude of the tension in the string attached to m (iii) Determine the magnitude of the tension between the pulleys.

Modern 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 rotating. A wind turbine has a total of 3 blades. Each blade has a mass of m = 5500 kg distributed uniformly along its length and extends a distance r = 44 m from the center of rotation. The turbine rotates with a frequency of f = 15 rpm. Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.

A bicycle wheel with a radius of 350 mm and a mass of (2.40x10^0) kg is spinning freely on a work stand at a rate of 2.0 rev/sec when a (1.0000x10^0) kg kitten jumps on it radially, holds on and starts spinning around. What is the new rotational velocity of the wheel in units of rev/s? Treat the wheel as a thin hoop. Give your answer with three significant figures.

A solid cylinder with mass m, radius R, and rotational inertia I (about its center) is released from rest and rolls down a ramp.  Friction between the bottom of the cylinder and the ramp causes the cylinder to roll without slipping.  The linear acceleration of the cylinder is a.  Which TWO of the equations below are correct for this scenario? The equations are in terms of m, I, R, and a, as well as f (the force of static friction between the cylinder and the ramp) and g.  (You must pick BOTH of them to get this question correct!) f = ma mg sin θ = ma mg sin θ - f = ma f R = I (a/R) mg sin θ - f = I (a/R) R mg sin θ = IaR

Please answer E16,E17

Two disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.58 m. Disk 1 has a moment of inertia I1 = 9.8 kg⋅m2. Disk 2 has a moment of inertia I2 = 5 kg⋅ m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity ω1,z = 21 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω2,z = -15 rad/s. The z component of their common angular velcoity is 8.837 rad/s How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small. I get I need to use kinetic energy equations of 1/2*I*w2 but…

what is the angular momentum of the of the Sun? It has a mass of 1.99 x 1030 kg. It has a radius of 696.3 x 106 m. It rotates with a linear velocity of 2200 m/s.