The object shown below is centered on the origin, and has a width of 20 cm in the x direction, 3 cm in the y direction, and 5 cm in the z direction. Around which axis does it have the lowest moment of inertia I?

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

From a solid sphere of mass M and radius R, a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is MR² (b) 32 √2π (a) 4MR² 9√3π (c) MR² 16 √2 G4MR² (d) 3√3π polit

The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ?h=0.156 m and mass 5.08 kg , and two thin crossed rods of mass 7.37 kg each. A farmer would like to replace his wheels with uniform disks ?d=0.0651 m thick, made out of a material with a density of 5530 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?

A yo-yo is made of two uniform disks, each of mass M and radius R, which are glued to a smaller central axle of negligible mass and radius 0.5R (see figure). A string is wrapped tightly around the axle. The yo-yo is then released from rest and allowed to drop downwards, as the string unwinds without slipping from the central axle.  Part (a)  Find the moment of inertia, I, of the yo-yo with respect to an axis through the common centers of the disks, in terms of the mass and radius.   Part (b)  Find the linear speed V of the yo-yo, after it has descended a distance H. Part (c)  Calculate the magnitude of the linear velocity V, in meters per second, of the yo-yo after it has fallen a distance 0.39 m

A circular cone with constant density 1, base radius 6, and height 8 is placed so the axis of symmetry is on the z-axis. A cylindrical hole of radius 1 is drilled through the axis of symmetry. Find the moment of inertia of the remaining shape. (The moment of inertia about the z-axis will be the same no matter where the shape is placed along the z- axis and whether the shape is pointing up or pointing down.)

The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius ?h=0.527 m and mass 5.65 kg, and two thin crossed rods of mass 7.80 kg each. Imagine replacing the wagon wheels with uniform disks that are ?d=5.88 cm thick, made out of a material with a density of 6910 kg/m3. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?

The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh=0.262 m and mass 4.32 kg, and two thin crossed rods of mass 9.09 kg each. Imagine replacing the wagon wheels with uniform disks that are td=6.51 cm thick, made out of a material with a density of 7370 kg/m3. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be?

Problem 3: 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. Part (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 0.11 m. sin() cos() tan() 7 8 9 HOME cotan() asin() acos() E 4 5 atan() acotan() sinh() 1 3 cosh() tanh() cotanh() END ODegrees O Radians Vol BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Part (b) Now calculate the moment of inertia of the skater (in kg m?) 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 0.825 m long rods extending straight out from the center of their body being rotated at the ends.

The wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius r = 0.368 m and mass 5.46 kg, and two thin crossed rods of mass 8.23 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0588 m thick, made out of a material with a density of 8290 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? 0.267 %3D Enter numeric value