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Introduction to Uniform Circular Motion. Derivation. There is slightly different from the derivation found in the text. For uniform linear motion we can find position by: When we have uniform circular motion, however, we can use. When given a circle: Where R is given as the radius (r).
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Derivation • There is slightly different from the derivation found in the text. • For uniform linear motion we can find positionby: When we have uniform circular motion, however, we can use
When given a circle: Where R is given as the radius (r). We know that: You can then take the derivative of the position in respect to time: and You can then take the derivative a second time: and
R-Form • 2 • , These are the MAGNITUDES of the acceleration, velocity and position vectors
Acceleration (Derivation) • Follow same pathway as with velocity, just use the second derivative taken.
Some Conclusions to be made: • Overall: Fundamental equation of circular motion
Centripetal vs. Centrifugal • Acceleration is always to the center • It is perpendicular to the motion • When this is happening, this is uniform circular motion • CENTRIPETAL MOTION/FORCE • The opposite: centrifugal