Starting from rest at the top, a small sphere rolls without slipping off a large fixed sphere. At what point will the small sphere leave the surface of the big sphere. In other words, what is the angle O?

A cylinder with moment of inertia I about its center of mass, mass m, and radius r has a string wrapped around it which is tied to the ceiling (Figure 1). The cylinder's vertical position as a function of time is y(t). At time t = 0 the cylinder is released from rest at a height h above the ground. Figure GO 1 of 1 Part A The string constrains the rotational and translational motion of the cylinder. What is the relationship between the angular rotation rate w and v, the velocity of the center of mass of the cylinder? Remember that upward motion corresponds to positive linear velocity, and counterclockwise rotation corresponds to positive angular velocity. Express w in terms of u and other given quantities. View Available Hint(s) W = ΠΑΠ ΑΣΦ Submit Part B Complete previous part(s) Part C ?

If small particle 'm' is placed a distance 'x' from the central axis of a solid disk of total mass M with 'r' radius, what would the be force?

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.

A rotating space station is said to create "artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. The outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. Randomized Variables d = 180 m If the space station is 180 m in diameter, what angular velocity would produce an "artificial gravity" of 9.80 m/s² at the rim? Give your answer in rad/s.

What is the angle between the vectors a = (10, -10, 0) and b = (-5, 5, 2), in radians?