A uniform sphere made of modeling clay has radius R and moment of inertia I1 for rotation about a diameter. It is flattened to a disk with the same radius R. In terms of I1, what is the moment of inertia of the disk for rotation about an axis that is at the center of the disk and perpendicular to its flat surface?

The three 'point' masses are as shown in the figure. m, = 2.0 kg at (x, y) =(0,0), m₂ = 3.0 kg at (4,3), and m3 = 4.0 kg at (8,0), respectively. What is the moment of inertia of the masses about the y axis? +y=3 m x=4 m

A uniform thin rod of mass M = 3.37 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass m = 0.219 kg, are attached to the ends of the rod. What must the length L of the rod be so that the moment of inertia of the three-body system with respect to the described axis is I = 0.975 kg-m? ? L = m M. m m L

A rod of mass 3m and length L can pivot about an axis through its center and perpendicular to the length of the rod as shown below. The rod has 2 point masses attached to either end, each of mass m. What is the moment of inertia of the rod + masses system about the axis through the center?               Needs Complete typed solution with 100 % accuracy.

Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius 2R) are connected by a thin, uniform rod of length 3R and mass M as shown in the Figure below. Find the moment of inertia about the axis through the center of the rod.         5.91 MR2     15.1 MR2     10.3 MR2     21.3 MR2

A rope with a negligible mass has two blocks that are suspended over a pulley, m, and M, as shown in the image.  The pulley can be considered as a uniform solid cylindrical disk. What is the equation for the net torque on the disc? Assume acceleration of blocks are a=(1/2)(9.8m/s2). What is the moment of inertia for this shape? (using the net torque equation from the above question, substitute the moment of inertia) The angular acceleration is correlated to the linear acceleration as α=r. Make the substitution into the torque equation in order to get the equation in terms of acceleration, α only.

A solid cylinder with a radius of 4.0 cm has the same mass as a solid sphere of radius R. If the cylinder and sphere have the same moment of inertia about their centers, what is the sphere’s radius?

A disk of radius R and thickness t has a mass density that increases from the center outward, given by p = po (r/R), where r is the distance from the axis of the disk. What is the moment of inertia about the disk axis in terms of M and R? O MR 2MR O sMP 3MR 5 O 2MR 3 5MR 3

Question 5 only.......

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 = 12 rpm. a)Calculate the total moment of inertia of the wind turbine about its axis, in units of kilogram meters squared.  b)Enter an expression for the angular momentum of the wind turbine, in terms of the defined quantities.  c)Calculate the angular momentum of the wind turbine, in units of kilogram meters squared per second.