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Relative Velocity and Acceleration in a Plane – Two points in the Same Rigid Link (Body)

In a Nutshell: Obtain the relative acceleration equation by taking the time derivative of each term in the relative velocity equation v_C = v_A + ω x r_AC with respect to frame F as shown in the

figure below.

dv_C / dt = d v_A /dt + d (ω x r_AC )/dt

Now dv_C / dt = a_C is the acceleration of point C with respect to the fixed frame, F

d v_A /dt = a_A is the acceleration of point A with respect to the fixed frame, F

and d (ω x r_AC )/dt contains two terms

dω/dt x r_AC and ω x d(r_AC) /dt

and as before d(r_AC) /dt = ω x r_AC since r_AC can only change in direction

So the relative acceleration equation becomes

a_C = a_A + dω/dt x r_AC + ω x ( ω x r_AC ) and for motion in the xy plane

ω x ( ω x r_AC ) = ωk x ( ωk x r_AC ) = ˗ ω² r_AC

Click here to continue with this discussion of relative acceleration.

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