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

A 35kg wheel is off-center, with its axle 3.4cm away from its actual center of mass, and it has a radius of 24cm. 84J of work goes purely into speeding it up from rest to 11.3 rad/s. What is the moment of inertia of the wheel?Do not actually solve the problem numerically or algebraically, just pick the one equation and define the relevant knowns and single unknown.

Determine the angular momentum of a 78-g particle about the origin of coordinates when the particle is at x = 4.9 m, y = -6.3 m, and it has velocity v = (3.51-80k) m/s. Find the x-component. Express your answer using two significant figures. Lx = ΜΕ ΑΣΦ Submit Request Answer ▼ Part B Find the y-component. Express your answer using two significant figures. Ly= ΜΕ ΑΣΦ Submit Request Answer Part C Find the z-component. Express your answer using two significant figures. ? kg-m²/s ? kg-m²/s

2. A yo-yo consists of two solid disks, each of mass M and radius 3R. The two disks are connected by a rod of radius R and negligible mass. Assume the yo-yo starts at rest. a. Use the view on the right to draw the extended free body 3R diagram for the yo-yo. b. What is the moment of inertia of the yo-yo about an axis through its symmetry axis? м м c. Write Newton's 2nd law for the yo-yo. Choose your coordinate system carefully. d. Write the rotational form of Newton's 2nd law for the yo-yo. Treat the center of mass as being at the axis of rotation. Choose the positive direction of the rotation so a is positive. e. The point where the yoyo is momentarily at rest is where the string contacts the rod of the yo-yo. Use this to obtain a relation between the acceleration of the center of mass and the angular acceleration. f. Determine the linear acceleration of the yo-yo.

1. Find the expression for the moment of inertia of a uniform, solid disk of mass M and radius R, rotated about an axis that goes through its center as shown in the diagram below. Hint: the moment of inertia of a thin ring is given by MR2. Divide the disk into a series of rings of radius r, mass dm, and thickness dr, then integrate over the rings. Your expression should only depend on the variables M and R. 99+

The three 220 gg masses in (Figure 1) are connected by massless, rigid rods. What is the triangle’s moment of inertia about the axis through the center? Express your answer to two significant figures and include the appropriate units.   What is the triangle’s kinetic energy if it rotates about the axis at 4.6 rev/srev/s ? Express your answer to two significant figures and include the appropriate units.

A bicycle wheel of mass M (all at the edges) and radius r is fixed about an axis through its center and is initially at rest. You wrap the wheel with a cord and attach a hanging weight of mass m to the cord. You release the weight and allow it to fall a distance d. The weight falls smoothly, and the cord does not slip over the wheel as it unwinds. a. (Write an expression for the angular acceleration α of the wheel in terms of the tension T of the cord.b. Write an expression for the linear acceleration a of the weight in terms of the tension T of the cord.c. (Using parts (a) and (b) find the linear acceleration in terms of M, m, and g.d. Write an expression for the linear speed v of the weight after it falls a distance d.e.  For M = 7.5 kg, r = 33 cm, m = 250 g, and d = 1.5 m, what is the rotational kinetic energy of the wheel afterthe weight has fallen?

The figure shows four orange point masses and four numbered blue axes. Each mass has m = 5.7 kg and is located on the corner of a square with sides of length 0.93 m. Axes 1 and 2 are perpendicular to the screen and pass through the indicated points. Axes 3 and 4 are in the plane of the screen. Calculate the assembly's moment of inertia I about axis 2. 2 I = 1 kg. m² 3 4

The three 160 g masses in (Figure 1) are connected by massless, rigid rods. a) What is the triangle’s moment of inertia about the axis through the center?  b) What is the triangle’s kinetic energy if it rotates about the axis at 5.2 rev/srev/s ? Express your answer with the appropriate units.

You have been given the following solid cone. The cone has a mass (m), height (h) and a base with a radius (r). Prove that the moment of inertia of the cone about its central axis is equal to (3/10)mr² (independent of h). N h