The three objects below have the same mass M and the same outer dimension (circular objects have diameters 2R and the square loop has sides of 2R).  The small circle at the center of each figure represents the axis of rotation for these objects.  Rank the moment of inertia of these objects about the axis of rotation from greatest to least.  Separate characters with a space. Enter your answer as A B C.

MII-1 Consider a solid disk of mass M and radius R, which has a uniform density. a) The disk is rotated about an axis that goes through its center and is perpendicular to its face, as shown in the diagram below on the left. Find a formula for its moment of inertia. Your answer should be a symbolic expression that only depends on the variables M and R. Hint: you will need to divide the disk into infinitesimal mass elements (dm) and then perform the integral: r?dm b) Suppose the radius of the disk is 12.5 cm and the mass is 1.75 kg. Use the formula from part a) to calculate a numerical value for the moment of inertia, in kg m2. c) Now the axis of rotation is moved from the center of the disk to the end of the disk, as shown in the diagram below on the right. Find an expression for its moment of inertia. Hint: theorem. As before, your answer should only depend on the variables M and R. d) Suppose the radius of the disk is 12.5 cm and the mass is 1.75 kg. Use the formula from part c) to…

Two blocks, on the frictionless incline as shown in the figure below, are connected by a string of negligible mass passing over a pulley of mass M, radius R and moment of inertia I= MR. What is the magnitude of the acceleration (in m/s) of the blocks if my = 5 kg ,m2 = 8 kg , M = 4 kg and e = 30? %3D T2 m1 m2 Lotfen birini seçin: a. 3.72 b. 3.37 c. 3.59 d. 4.00 e. 4.15

A solid spherical jewel rolls smoothly from rest down a ramp. The jewel descends a vertical height of 1.2m to reach the bottom of the ramp. What is the jewel's speed at the bottom of the ramp? Hint: This problem has nothing to do with elasticity as we did not formally cover that topic, and the inertia of a solid sphere is found by 2/5 m r2

Suppose we want to calculate the moment of inertia of a 65.5 kg skater, relative to a vertical axis through their center of mass. a.  First calculate the moment of inertia (in kg⋅m2) when the skater has their arms pulled inward by assuming they are cylinder of radius 0.125 m.  b.  Now calculate the moment of inertia of the skater (in kg⋅m2) with their arms extended by assuming that each arm is 5% of the mass of their body. Assume the body is a cylinder of the same size, and the arms are 0.875 m long rods extending straight out from the center of their body being rotated at the ends.

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. Draw a free body diagram and explain if the tensions in the two strings equal? Why? Why not? To solve the problem, why can’t I use the system approach and write the equation for M and m at the same time? Please write the equations that will help solve for T1 and T2

Three small steel balls are connected by rigid, very light rods as shown in the figure. What is the moment of inertia if the object rotates about the x-axis? If we apply a force of 200. N to the most massive ball such that the object will rotate counterclockwise about the x-axis, what angular acceleration will result?

An old vinyl record is played on a turntable that turns at a rate of 45 rotations per minute. Find the angular speed in radians per second. Give your answer as a fraction and do not include units. Keep your answer in terms of π if necessary.

In this problem you will be given the mass and description of various objects and will determine their moments of inertia I. All results are of the form X * M R2. You will find the numerical value of X.What is the moment of inertia for a ring with mass 2 M and an axis of rotation through the center of the ring (perpendicular to the plane of the ring) with radius 2 R. M R2   Tries 0/3   What is the moment of inertia for a disk with mass 3 M and an axis of rotation through the center of the disk with radius 2 R. M R2   Tries 0/3   What is the moment of inertia for a hollow sphere with mass 1 M and an axis of rotation through the center of the sphere with radius 3 R. M R2   Tries 0/3   What is the moment of inertia for a solid sphere with mass 4 M and an axis of rotation through the center of the sphere with radius 3 R. M R2