7-3 Circular Motion

As an object travels in uniform circular motion Its tangential speed remains constant The direction of its velocity is constantly changing How is there an acceleration if the speed is constant? because the direction changes (see b above) In what direction does the acceleration point? in the same direction as ∆v toward the center of the circle

Centripetal Acceleration: so-called because the acceleration points toward the center “centripetal” – “center seeking” where a c = centripetal acceleration v = tangential speed r = radius of the circle Calculating Centripetal Acceleration:

Centripetal Acceleration using period, T Period, T is the time that it takes for one revolution The tangential speed, v would be calculated by d/t : v = circumference of circle time for one revolution v = 2 π r / T So centripetal acceleration would be calculated: a c = (2 π r / T) 2 / r a c = 4π 2 r / T 2

Cause of centripetal acceleration: Net Forces cause accelerations There must be a centripetal Force, F c causing the centripetal acceleration Thus, to calculate F c :

“Centrifugal Force” A fictitious force Arising from Newton’s first Law

Formulas for Circular Motion a c = 4π 2 r / T 2 v = 2 π r / T