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 ac = centripetal accelerationv = tangential speedr = 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 circletime for one revolution

v = 2 π r / T

So centripetal acceleration would be calculated:

ac = (2 π r / T)2 / r

ac = 4π2 r / T2

Cause of centripetal acceleration:

• Net Forces cause accelerations

• There must be a centripetal Force, Fc causing the centripetal acceleration

• Thus, to calculate Fc :

“Centrifugal Force”

• A fictitious force

• Arising from Newton’s first Law

Formulas for Circular Motion

ac = 4π2 r / T2

v = 2 π r / T