Conceptual Physics

(Sean Pound) #1

14.4 - Angular frequency


Angular frequency: Frequency measured in


radians/second.


In the equation for SHM shown in Equation 1, the parameter Ȧ is the angular frequency
and it is the coefficient of time in the equation for SHM. Its units are radians per second.


The angular frequency equals 2 ʌtimes the frequency. The relationship between
frequency and period can be used to restate this equation in terms of the period. Both
these equations are shown in Equation 2.


You may have noticed that Ȧalso stands for the angular speed of an object moving in a
circle, which is measured in radians per second, as well. If an object makes a complete
loop around a circle in one second, its angular speed will be 2 ʌ radians per second.
Similarly, an object in SHM that completes a cycle of motion in one second has an
angular frequency of 2 ʌ radians per second. This is indicative of a relationship between
circular motion and SHM that can be productively explored elsewhere.


Angular frequency


x(t) = A cos (Ȧt + ij)


Angular frequency is Ȧ


Units: radians per second (rad/s)


Angular frequency and period


Ȧ = 2ʌf


Ȧ = 2ʌ/T


T = period


f = frequency


The function x(t) = A cos(Ȧt)


describes this graph. What is the


angular frequency, Ȧ?


Ȧ = 2ʌ/T


T = 3.5 seconds


Ȧ = 2ʌ/3.5


Ȧ = 1.8 rad/s


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