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Relative Velocity and Acceleration in a Plane – (continued)

In the fixed frame of reference, F,

dr_C /dt = dr_A/dt + dr_AC /dt

The result is as follows: v_C = v_A + v_AC

where v_C = dr_C /dt is the velocity of point C with respect to the fixed frame, F

v_A = dr_A/dt is the velocity of point A with respect to the fixed frame, F

v_AC is the velocity of point C with respect to point A in the fixed frame

Physical Interpretation of v_AC :

Position yourself at point A in a non-rotating chair and look at point C. The distance from A to C is constant. So the only motion of C that you see is a rotation of point C about point A.

Click here to see that v_AC is equal ω x r_AC (cross product) where ω = dθ/dt k is the angular velocity of the rigid link B in the fixed frame F and r_AC is the vector from A to C.

v_C = v_A + ω x r_AC which is the “relative velocity equation”

Click here for examples.

Click here to go to a discussion on instantaneous center of zero velocity.

Click here to continue with discussion of relative accelerations.

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