<p>So today in class we were given this problem from a previous AP test that has me stumped. I believe that I figured out parts i and II of part A, but I am having trouble on the rest. If anyone that is good with centripetal acceleration/ conservation of energy help me, I would greatly appreciate it! Thanks.</p>
<p>A particle of mass m slides down a fixed, frictionless sphere of radius R. starting from rest at the top.
a. In terms of m, g, R. and theta, determine each of the following for the particle while it is sliding on the sphere.
i. The kinetic energy of the particle
ii. The centripetal acceleration of the mass
iii. The tangential acceleration of the mass
b. Determine the value of theta at which the particle leaves the sphere.</p>