The point particle m slides frictionlessly along a circular wire of radius R in the vertical xy plane (the point particle cannot be separated from the wire as it is inserted into the wire like a ring). Gravity is g = − gj. a)The particle v0 is ejected with its initial velocity (in Figure I, the x component of linear velocity is positive). The line connecting the particle to the center of the circle makes an angle Φ0 with the x-axis at t = 0 (0 > Φ0 > − π/2, fourth quadrant). Find the initial acceleration of the particle in terms of σˆ and Φˆ. b) The wire rotates around the vertical y-axis with constant angular velocity Ω (fig. 1). If Ω> Ωc, then Φ''>0 will be at Φ= Φ0. Otherwise (Ω<Ωc) initially Φ'' will be negative. Find a relationship between the angular velocity Ωc and Φ0. c) Assume Ω > Ωc. Find the absolute acceleration of the particle in terms of Ω, R, Φ', Φ'' based on σˆ , Φ , σˆ x Φ = k.