The particle has a constant speed
given by ωR
when it moves on the circumference of a circle with
radius R
and yet it is accelerated
with an acceleration given by
ω2R.
Consequently, the particle of mass m
feels a force according to
Newton's second law
which is given by
F = ma = mω2R
The necessity for this acceleration is not for an increase, or for a
decrease, in speed, but for the changes in the direction of the velocity.
This is most clearly formulated in
Newton's first law
which states that an object that is in motion
will not change its velocity, neither magnitude, nor direction,
unless an unbalanced force acts upon it.
Hence, a particle will only perform a curved
motion when some force is applied
to it.
For example, a cord attached to the particle, friction forces,
gravitation in the case of planets which orbit the Sun
and satellites which orbit the Earth,
or electromagnetic forces for electrons which orbit the nuclues of an atom.
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