(adsbygoogle = window.adsbygoogle || []).push({}); 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

I_{center}= m h^{2}/12; moment of inertia of stick

3. The attempt at a solution

Sum of horizontal forces:

m a_{x}= -F_{A}

a_{x}= -F_{A}/m

Sum of vertical forces:

ma_{y}= -mg + F_{N}= 0

Sum of torque

T = I u = 0.5 h F_{N}sin(d) - 0.5 h F_{A}cos(d)

u = 0.5 h ( mg sin(d) - F_{A}cos(d) ) / ( m h^{2}/12 )

u = ( 6 / m h )( mg sin(d) - F_{A}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.

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# Homework Help: [FBD] Stick balancing

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