EXAMPLE 4: Newton’s 2nd 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.






r = constant



(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