Example 4.3-2

 

Referring to the figure, derive the equation for the velocity and acceleration of point A using the following equations for fixed-axis rotation and relative motion.

 

Fixed-axis rotation equations.

 

v_A = ω x r_A/O     a_A = α x r_A/O - ω²r_A/O

 

Relative motion equations.

 

v_A = v_B + v_A/B     a_A = a_B + a_A/B

 

 

What is the velocity and acceleration of point A if point B is fixed and A is rotating about B?

 

v_A = ω x r_A/B
v_B = ω x r_B/A
v_A = ω x r_A/O

 

 

 

a_A = α x r_A/B + ω²r_A/B
a_A = α x r_A/O - ω²r_A/O
a_A = α x r_A/B - ω²r_A/B

 

 

 

Knowing the velocity and acceleration of point B, what is the absolute velocity and acceleration of A?

 

v_A = ω x r_A/B
v_A = v_B + ω x r_A/B
v_A = v_O + ω x r_A/O

 

 

 

a_A = a_B + α x r_A/B - ω²r_A/B
a_A = α x r_A/B + ω²r_A/B
a_A = a_B + α x r_A/B + ω²r_A/B