[FBD] Stick balancing

1. Nov 20, 2008

saltine

1. The problem statement, all variables and given/known data

Find the linear and angular accelerations given that FA is the applied force.
v is the current linear velocity and w is the current angular velocity.
r is the radius of the stick.
h is length of the stick.
d is angle from the vertical axis.

2. Relevant equations
a = dv/dt; linear acceleration
u = dw/dt; angular acceleration
Icenter = m h2/12; moment of inertia of stick

3. The attempt at a solution
Sum of horizontal forces:
m ax = -FA
ax = -FA/m

Sum of vertical forces:
may = -mg + FN = 0

Sum of torque
T = I u = 0.5 h FN sin(d) - 0.5 h FA cos(d)
u = 0.5 h ( mg sin(d) - FA cos(d) ) / ( m h2/12 )
u = ( 6 / m h )( mg sin(d) - FA cos(d) )

Is this correct?

Shouldn't the vertical acceleration be non-zero? Because if w and u are non-zero, and the finger maintains at the same height, then the center of mass of the stick must be moving. What is wrong with the above?

- Thanks
And thank you for replying to my other thread. There are so many threads I thought I shouldn't bump the one that was solved.