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A solid sphere of mass 2kg and redius 1m is free to rotate about an axis passing through its center. Find a constant tangential force f required to rotate the sphere with 10 rad/sec in 2sec . Also find number of rotation made by sphere at that time interval. |
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Answer» energy of rotation is E = 1/2 I w^2, where I is the moment of inertia and w the ANGULAR frequency of rotation. The moment of inertia of a solid sphere of mass 2kg and radius 1m is: Is = 2/5 *2 *1^2, WHILST that of a solid cylinder is of mass 2kg radius 1mabout its central AXES is independent of its height and equals IC = 1/2 *2*1^2 So we want to equate the energies through 1/2 *2/5 *2*1^2 * (w_sphere)^2 = 1/2 * 1/2* 2*1^2 * (w_cyl)^2 (w_cyl)^2 = 4/5 (w_sphere)^2 w_cyl = +-sqrt(4/5) ω (NOTE that the energy of rotation is independent of the direction of rotation, so we have two solutions).Dr. |
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