Example 2: Newton’s 2^{nd} law
A
bead of mass m moves on a bar. The
bar is shaped as shown in the figure so that _{}. If the bar is smooth and the particle is released from rest
at the position _{}, calculate the equation of motion of the bead and the force
applied by the bar on the bead at _{}.
Solution:

Kinematics relation:
_{}
_{}
_{}
_{}
_{}
Kinetics:
_{}
_{}
Equation of motion:
_{}
_{}
_{}
Subtract
to get
_{}
_{}