1983M3. 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 θ, 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 θ at which the particle leaves the sphere.