EXAMPLE 4: Newton’s 2^{nd} law

A particle starts at A with an initial velocity of _{}, and moves down the smooth circular ramp up to point B when
it separates. Obtain the equation of
motion of the particle and the angle _{} at which it
separates.
Solution:

Kinematics:
r = constant
_{}
Kinetics:
_{}
_{}
(2) is the equation
of motion
At point of separation, N=0
_{}
Integrating (2) using
_{}
we get
_{}
_{}
_{}
By the initial conditions at A
_{}
_{}
Substitution of C into (4) gives
_{}
Solving for _{} and substituting into
(3) gives
_{}