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SOLVED:A solid sphere (radius =R ) rolls without slipping in a cylindrical trough (radius =5 R ) as shown in Figure P15.56. Show that, for small displacements from equilibrium perpendicular to the length of the trough, the sphere executes simple harmonic motion with a period T=2 π√(28 R / 5 g). (FIGURE CANT COPY)
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A sphere of radius R, at a distance r from the observer, has a uniform brightness B. The specific intensity is equal to B if the ray intersects the sphere, and zero otherwise. Use equation (3.41) to express the flux ℱ in terms of brightness B and , the angle at which a ray from the observer is tangent to the sphere (i.e., 2 is the angle subtended by the sphere as seen from the observer). Show that on the surface of the sphere, ℱ=πB (eq. 3.7). | Numerade
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educationexplaning on Instagram: "The surface area of a sphere is calculated using a simple mathematical formula based on its radius. If a sphere has a radius r, its surface area is given by 4πr². This formula comes from the idea that a sphere’s curved surface can be related to the area of multiple circular slices wrapped around it. No matter how large or small the sphere is, its entire outer surface is always four times the area of a circle with the same radius, making this one of the most eleg
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