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As you already know, when the speed of a point moving in a circle is constant, its motion is called uniform circular motion.
As you also already know, even though the speed of the point is constant, the velocity is not constant. The velocity is constantly changing because the direction of thevelocity vector is constantly changing.
The period
The amount of time required for the point to travel completely around the circle is called the period of the motion.
The frequency
The frequency of the motion, which is the number of revolutions per unit time, is defined as the reciprocal of the period. That is,
frequency in rev per sec = 1/(period in sec per rev), or
f = 1/T
where
The speed of a point moving completely around the circle is equal to the distance traveled divided by the time.
sT = 2*pi*r/T, or
sT = 2*pi*r*f
where
We know from before that
sT = w * r, or
w = sT/r
Therefore, by substitution from above,
w = 2*pi*r*f/r = 2*pi*f, or
the angular velocity in radians per second is the product of 2*pi and the frequency in revolutions per second.
where
The SI unit for frequency
The SI unit for frequency is hertz (Hz) where 1 Hz is equal to one revolution per second or one cycle per second.
Facts worth remembering
w = 2*pi*f
where
The SI unit for frequency is hertz (Hz) where 1 Hz is equal to one revolution per second or one cycle per second
In an earlier module, you learned how to subtract vectors and; demonstrate that the acceleration vector of an object moving with uniformcircular motion always points toward the center of the circle. However, in that lesson, we did not address the magnitude of the acceleration vector. We will dothat here.
A very difficult derivation
Deriving the magnitude of the acceleration vector depends very heavily on the use of vector diagrams, complex assumptions, complicated equations.Unfortunately, this is one of those times that I won't be able to present thatderivation in a format that is accessible for blind students. In this case, blind students will simply have to accept the final results in equation form anduse those equations for the solution of problems in this area.
Facts worth remembering
Ar = v^2/r, or
Ar = (w^2)*r
where
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