Two uniform solid spheres have the same mass, but one has three times the radius of the other. The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is Express your answer as a whole number.
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- The photo shows a high-wire walker striding confidently along a steel cable stretched nearly half a kilometer above the bottom of a gorge in the Grand Canyon. If he tips slightly to the side, a gravitational torque will start to rotate his body even farther—which is clearly not good. To help him balance, he carries a long, heavy pole. This increases the moment of inertia, which results in a smaller angular acceleration, giving him more time to recover his balance.Model the man’s body as a 1.8-m-long, 88 kg, uniform rod. The pole is 9.1 m long, with a mass of 20 kg. What is the moment of inertia of his body? Of the pole?Consider a flat disk of radius 15cm. The mass per unit area is given as σ = 4r3 Calculate the disks mass and moment of inertia.The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center (Figure 1). When his hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass 8.0 kg. When outstretched, they span 1.6 m ; when wrapped, they form a thin-walled hollow cylinder of radius 26 cm. The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.4 kg⋅m2. If his original angular speed is 0.30 rev/s, what is his final angular speed?
- Determine the moment of inertia of a solid homogeneous cylinder of radius R and length L with respect to a diameter in the base of the cylinder.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 l?Twin skaters approach one another as shown in the figure below and lock hands. (a) Calculate their final angular velocity, given each had an initial speed of 1.60 m/s relative to the ice. Each has a mass of 70.0 kg, and their centers of mass are 0.850 m from their locked hands. You may approximate their moments of inertia to be that of point masses at this radius. rad/s(b) Compare the initial and final kinetic energy. Ki Kf =