Circular Motion

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Circular Motion
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RATES OF REVOLUTION

• T PERIOD time for 1 revolution

second
SI unit for period
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f FREQUENCY
number of revolutions per time
SI unit
rev./second
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PERIOD vs. FREQUENCY
T seconds/revolution f revolutions/second
T 1/f
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Direction of Motion tangent to path
v is the linear (tangential) speed
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LINEAR (TANGENTIAL) SPEED
(assuming a constant speed) v (speed)
distance /time
For 1 revolution v
circumference/period
2pr T
v
2prf
v
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ACCELERATION FOR CIRCULAR MOTION?

• If the speed is constant , is there acceleration?

YES.
Since the direction of motion changes, the
velocity is not constant.
The direction of the acceleration is the same as
the direction of the force.
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CENTRIPETAL FORCECENTRIPETAL ACCELERATION

• Force and acceleration act towards the center.

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Velocity along tangent Acceleration Net Force
towards center
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Centrifugal force a description of the
objects inertia. Not a real force.
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using similar triangles
?v --- v
L -- r
?v Lv/r
v distance /time L/t
L vt
?v v2t/r
a ?v/t
v2/r
Fc mv2/r
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Equations for Centripetal Acceleration and Force

• ac v2 Fc mv2
• r r
• Since v 2pr
• T

ac
4p2r T2
4p2r m T2
Fc
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Find the magnitude of the acceleration of the
Moon around the Earth.
Earth-Moon distance 384 x 103 km
period of Moon around Earth 27.3 days