Acceleration & Circular Motion

• We now know the direction of the acceleration (toward the center). How big is it?

v2

v1

R

v1

v2

?v

??

??

For small angles ?????measured in radians:

?v = v??

| v1 | = | v2 | = v

• To find the acceleration, we need to know how ?? is related to ?t :
  • For one revolution, the angular displacement is: ?? = 2???(radians)
  • The time required for one revolution (period) is: ?t = 2?R / v
  • Therefore,
    
  • Combining these equations:

??????t = v / R

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