The force
F=mω2R
which holds the particle in place when it orbits at
constant speed
given by ωR
the center of a circle with
radius R,
is called centripetal force.
Its relation to the speed of the particle is given by
F = mω2R
= m (ωR)2 /R
= m v2 /R
For example, the Earth has a mass of
M=6.0×1024
kg, it makes one revolution (2π)
around the Sun in one year
(3.16×107
seconds).
Hence
ω = 2π/(3.16×107 s)
= 2.0×10-7 s-1
The radius of its orbit equals 150 million kilometers
(1.5×1011
meters)
Hence, the force needed to keep the Earth in place equals
F = Mω2R
= (6.0×1024 kg) ×
(2.0×10-7 s-1)2 ×
(1.5×1011 m)
= 3.6×1022 N
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