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# Mechanics Circular motion in a sphere problem watch

1. A particle P of mass m is free to move inside a sphere with centre O and radius r.The particle starts from the lowest point, directly below O, with a speed v. As longas the particle stays on the inner surface of the sphere, its position can be described in terms of the angle Ɵ between the line OP and the vertical.

(a) Find the particle speed as a function of Ɵ.
(b) Find the normal reaction between the particle and the surface of the sphere.
(c) Show that the particle remains in contact with the sphere through a complete revolution as long as v ≤ sqrt(5*gr)
(d) Show that if sqrt(2rg) < v < sqrt(5rg) then the particle will lose contact with the sphere. What happens when v < sqrt(2rg)?

Question above. I am stuck on part (d). My thoughts are that I need to show that the resultant = mg alone (ie it is now a projectile and thus must have lost contact). But how do I account for Ɵ?
2. bump

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