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Physics 101: Lecture 11
Centripetal Force
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Brief Review of Chapters 1-4
Textbook Chapter 5
ÎUniform circular motion :
satellites in circular orbits, apparent weightlessness and
artificial gravity
Physics 101: Lecture 11, Pg 1
Centripetal Force
Centripetal acceleration:
ac
v2
=
R
Acceleration is the result of a net-force acting on an object.
In case of ac this net-force is called centripetal force, Fc:
Magnitude of Fc: Fc= Σ F= m ac= m v2/R
Direction of Fc: always points towards the center of
the circle
Define frequency f, period T, angular velocity ω:
ac = (2π f ) R
2
2
 2π 
ac =   R
T 
ac = ω 2 R
The period T is the time required to travel once around the circle,
ie to make one complete revolution: T=2π R/v
Physics 101: Lecture 11, Pg 2
Satellites in Circular Orbits
Satellites in circular orbits are examples of uniform circular
motion.
What provides the centripetal force ?
The gravitational pull of the earth: Fc= G M m/r2 = mv2/r
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⇒
Orbital speed of statellite : v = (GM/r)1/2 => v does not depend on
mass of satellite !
Synchronous satellites: Orbital period T=1 day = time it takes for the
earth to turn once around its axis.
=> Satellite always appears to be at a fixed position in the sky ->
stationary relay stations for communication signals sent up from
earth.
Physics 101: Lecture 11, Pg 3
Synchronous Satellites
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To serve as stationary relay station the
satellite must be placed at a certain
height above the earth surface:
T=1 day=8.64 x 104 s = 2π r/v and
v=(G M/r)1/2
⇒ r3/2=T (GM)1/2/(2π) => r=4 x 107 m
⇒ H=r-rE=3.6 x 107 m = 22300 miles
Physics 101: Lecture 11, Pg 4
Circular Motion: More Examples
Apparent weightlessness:
Apparent weight in a satellite is zero just as in a free
falling elevator :
Person and scale fall with the same acceleration
towards the center of earth => they cannot push against
each other.
z Artificial gravity:
In a rotating space laboratory a push on
a persons feet equal to mg can be simulated by the
centripetal force if v = (r g)1/2.
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Physics 101: Lecture 11, Pg 5