About what axis will a uniform, balsa-wood sphere have the same moment of inertia as does a thin-walled, hollow, lead sphere of the same mass and radius, with the axis along a diameter?
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About what axis will a uniform, balsa-wood sphere have the
same moment of inertia as does a thin-walled, hollow, lead sphere of the
same mass and radius, with the axis along a diameter?
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- You have a solid cylinder, a hoop, a solid sphere, and a hollow sphere all with the same mass and radius. If you apply an identical torque to each, which will experience the greatest angular acceleration? Which will experience the lest?A solid cylinder of uniform density of radius 2 cm has mass of 50 g. If its length is 10 cm, Calculate its moment of inertia about (i) its own axis of rotation passing through the centre. (ii) an axis passing through its centre and perpendicular to its length.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?
- As a physics demonstration, a special bowling ball is made so that it can be rotated about its center of mass to get a feel for how "big" a moment of inertia of 1 kg⋅m2 is. The average bowling ball has a weight of 15.4 lbs and a circumference of 26.3 inbut it does not have a moment of inertia equal to 1 kg⋅m2.Since the sporting goods manufacturer has no understanding of how "big" 1 kg⋅m21 is, calculate the diameter ? demo of the demo bowling ball, in inches, that it will need to manufacture. Assume that bowling balls are solid, with a constant density. D of demo required in inches.A 575-gram basketball with a radius of 10.5 cm is a uniform hollow sphere that rolls without slipping along a horizontal surface of a floor such that the translational speed of the center of mass is 3.50 m/s. (a) What is the moment of inertia of the basketball? (b) What is the angular speed about the center of mass of the basketball as it rolls along the floor? (c) The basketball then reaches an incline that makes an angle of 30.0° above the horizontal. If we ignore any energy losses due to dissipative forces, then to what maximum vertical height above the floor will the basketball reach? Include a diagram of the situation.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 =