Consider the region inside the sphere x2 + y² + z2 = 9, but outside the cone z = r. If the density is uniform, K, find the moment of inertia with respect to the z-axis. Answer. 81K V2/2.
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- Two uniform, solid spheres (one has a mass M and a radius R and the other has a mass M and a radius Rb=2R are connected by a thin, uniform rod of length L=2R and mass M. Note that the figure may not be to scale. Find an expression for the moment of inertia I about the axis through the center of the rod. Write the expression in terms of M, R, and a numerical factor in fraction form.A solid ball of radius r begins to roll down a hemisphere with radius R. Find the angular speed of the ball at the moment it leaves the surface of the hemisphere. Obviously, r < R.A child sits on a merry‑go‑round that has a diameter of 6.00 m. The child uses her legs to push the merry‑go‑round, making it go from rest to an angular speed of 18.0 rpm in a time of 37.0 s. What is the angular displacement Δθ of the merry‑go‑round, in units of radians (rad), during the time the child pushes the merry‑go‑round?
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