21-70. The 1-lb top has a center of gravity at point G. If it spins about its axis of symmetry and precesses about the vertical axis at constant rates of w, = 60 rad/s and w, = 10 rad/s, respectively, determine the steady state angle 0. The radius of gyration of the top about the z axis is k. = 1 in., and about the x and y axes it is k, = k, = 4 in. w, = 10 rad/s w, = 60 rad/s 3 in.
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- A star of radius R = 2.3 * 108m rotates with an angular speed v = 2.4 * 10-6rad>s. Ifthis star collapses to a radius of 20.0 km, find its final angular speed. (Treat the star as if itwere a uniform sphere, and assume that no mass is lost as the star collapses.)A star originates as a large body of slowly rotating gas.Because of gravitational attraction, this large body of gas slowly decreases in size.You can assume that no external forces are acting.Which one of the following statements correctly describes what happens as the radius of the body of gas decreases? Both the moment of inertia and the angular velocity increase. Both the angular momentum and the angular velocity increase. The angular momentum increases and the angular velocity decreases. Both the angular momentum and the angular velocity decrease. The angular momentum remains constant and the angular velocity increases.A small 4-lb collar C can slide freely on a thin ring of weight 6 lb and radius 10 in. The ring is welded to a short vertical shaft, which can rotate freely in a fixed bearing. Initially, the ring has an angular velocity of 35 rad/s and the collar is at the top of the ring (0 = 0) when it is given a slight nudge. Neglecting the effect of friction, determine (a) the angular velocity of the ring as the collar passes through the position 0 = 90°, (b) the corresponding velocity of the collar relative to the ring.
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- • Problem 3.22 The potential energy between the atoms of an hydrogen molecule can be modelled by means of the Morse potential -2(r – ra) (r V (r) = V exp 2 еxp where Vo = 7 × 10 12 erg, ) = 8 x 10-º cm and a = 5 x 10-º em.Please don't provide handwritten solution. Three identical full spheres of mass 3.1kg and Radius R=2.9m are welded together in such a way that the centres of each of them are at (R,0,0), (3R,0,0) and (5R,0,0). The whole system rotates in +XY plane about the axis parallel to z axis and passing through point (6R,0,0). Find the moment of inertia of the whole system. State your answer to the nearest tenth of kgm2.WEE21 2(0.ss 26.ss) O= 400,9 %3D 6) .2m 2 metal disks, one with radius 20 cm and mass 0.5 kg, and the other with radius Sm 50 cm and mass 1 kg, are welded together and mounted on a frictionless axis through their common center. A light string is wrapped around the edge of the smaller disk, and a 1.50 kg block is suspended from the free end of the string. If the block is released from rest at a distance of 2.40 m above the floor, what is its speed just before it strikes the floor? answer in m/s, use g=10 m/s? laib totion ed R2 不 R 1.50 kg a) 2,32 b) 3,84 C) 8,41 d) 4.47