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

 

 

Key Concepts:  Motion of any object depends on the frame of reference in which that

motion is measured.  Imagine you are on a chair at the center of a merry-go-round watching

a friend on another chair at the outer edge of the merry-go-round.  Once the merry-go-round

starts turning, from your perspective, your friend is still not moving - no relative velocity nor

relative acceleration with respect to you.  Actually as the merry-go-round speeds up to its

terminal speed, your friend has both a velocity and an acceleration with respect to a fixed

frame of reference even though the distance and direction of your friend does not change

relative to you.  Velocity is a change in the position vector and acceleration is a change

in the velocity - both referred to a frame of reference.

 

 

In a Nut Shell:  Start by examining the motion of two points on the same rigid link with respect to a fixed frame of reference xy with origin O.  Let  rA  be the position vector of point A with respect to the fixed frame F, rC  be the position vector of point C with respect to the fixed frame, F, and rAC  be the position vector of C relative to point A all at any time t.    Click here for a discussion of strategy.  

See the figure below.                      

 

 

                              

 

 

By vector addition,

 

                rC  =    rA  +  rAC    =   position vector of  C  at any time  t

 

Now take the derivative of each vector with respect to time in the fixed frame of reference, F.

 

 

Click here to continue discussion of the kinematics of relative velocity.            

 

Click here for details on construction of velocity and acceleration vectors in planar motion.

 

 

 


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