Maximum Angular Velocity
In linear motion maximum velocity is the velocity of light, denoted by “c”. This principle had been extended to circular motion and it is assumed that the maximum angular velocity is C/R. Bases on this assumption when a particle is rotating with maximum angular velocity around a unit circle, (where R=1), its acceleration will be c2/R.
On the other hand, there is the well-known statement that; “velocity of the representation point in hodograph is acceleration of the particle in its path.” (Mater and Motion.) Thus the representative point in hodograph will have a velocity more than “c”, and we are confronted with a velocity more than the velocity of light.
However, there is an alternative approach, since the velocity of the representative point in hodograph cannot be more than “c”, it may be argued that the limit of acceleration in circular motion is “c”. In this way, as acceleration in circular motion will not be more than “c”, maximum angular velocity will be √c/r.
Rω2= C, ω= √C/R.
Similarly, the maximum angular velocity of therepresentative point in hodograph will be; c/√c =√c
JavadRajabzadeh
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Maximum angular velocity
1. Maximum Angular Velocity
In linear motion maximum velocity is the velocity of light,
denoted by “c”. This principle had been extended to
circular motion and it is assumed that the maximum
angular velocity is C/R. Bases on this assumption when a
particle is rotating with maximum angular velocity around a
unit circle, (where R=1), its acceleration will be c2/R.
On the other hand, there is the well-known statement that;
“velocity of the representation point in hodograph is
acceleration of the particle in its path.” (Mater and
Motion.) Thus the representative point in hodograph will
have a velocity more than “c”, and we are confronted with
a velocity more than the velocity of light.
However, there is an alternative approach, since the
velocity of the representative point in hodograph cannot be
more than “c”, it may be argued that the limit of
acceleration in circular motion is “c”. In this way, as
acceleration in circular motion will not be more than “c”,
maximum angular velocity will be √c/r.
Rω2
= C, ω= √C/R.
Similarly, the maximum angular velocity of
therepresentative point in hodograph will be; c/√c =√c
JavadRajabzadeh
