1. The problem statement, all variables and given/known data Suppose a non-uniform circular motion where a particle of mass "m" is attached to a string, which rotates on a vertical plane. Once an initial velocity is provided to the particle at the lowest point of the trajectory, no further forces act on the particle. (Air drag is negligible) Which is the minimum velocity that the particle requires to reach the highest point of the trajectory? If initial velocity is two-times the one we calculated in question 1, what would be the velocity in the highest point? Calculate the acceleration too: Calculate the maximum height the particle can reach if the velocity is half the one calculated in 1. Calculate the initial velocity if the particle rotates only 2[itex]\Pi[/itex]/3 radians: 2. Relevant equations [itex]1/2[/itex]mv^2bottom=[itex]1/2[/itex]mv^2top+mg2r Centripetal acceleration=(v^2)/(r) v=ωr 3. The attempt at a solution For no.1 , given that KE is fully transformed into potential energy at the highest point of the circle,KE is 0 in the right side of the equation so: v=2√(gr) For number 2, if velocity is 4√(gr) then [itex]1/2[/itex]m(4√(gr))^2=[itex]1/2[/itex]mvtop^2+mg2r →vtop=2√(3gr) So I tried to calculate the centripetal acceleration and I got an=(2√(3gr)/r But know I don't know how to calculate the tangential acceleration with only the values I know and now I'm stuck on this problem. Pleasse help me!