Relative acceleration equation can be derived from the the relative velocity equation,
vB = vA
Differentiate with respect to time to give
aB = aA + aB/A
Just like the relative velocity equation, the relative acceleration equation can be separated into linear motion and angular motion. However, it is important to note that the angular motion has two components, tangential and normal acceleration.
3-Bar Acceleration Motion
Each rotation term can be written as cross products, giving
aB = aA + ωAB × (ωAB × rAB) + αAB × rAB
This form shows that the relative acceleration is composed of the translating motion of base point A and the rotating motion of point B about A.
For plane motion, the normal rotation terms
can be simplified as -ω2r giving
aB = aA - ω2rAB + α × rAB
Another way to write the relative acceleration equation is
aB = aA - ω2ren + αret
Practice Homework and Test problems now available in the 'Eng Dynamics' mobile app
Includes over 400 problems with complete detailed solutions.
Available now at the
Google Play Store and
Apple App Store.