ro. Moreover, the differential of the vector acts along a tangent to the curve followed during the motion. Hence, velocity at a moment within a movement along a path is tangential to the path; acceleration (change in velocity) is tangential to velocity.
For example, an automobile driven at a velocity of 30 miles per hour (44 ft/sec) in a 1,000 foot circle does not have a zero acceleration (just because the scalar speed is not changing). The car is changing direction (around the circle) at every instant, so the velocity is changing at every instant, because velocity is a vector having both magnitude and direction. The auto's acceleration normal to (perpendicular to, i.e., inward from) the direction of movement is, indeed, v2/r or 442/1,000 or 1.94 feet per second squared.
While the study of dynamics is headed ultimately toward kinetics--a study of forces that make things move or that result from motions of bodies, theoreticians of dynamics start with kinematics. Higdon
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