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20 Ιουλ 2022 · \(\overrightarrow{\mathbf{a}}_{r}(t)=-r \omega^{2}(t) \hat{\mathbf{r}}(t)\) uniform circular motion . Because the speed \(v=r|\omega|\) is constant, the amount of time that the object takes to complete one circular orbit of radius r is also constant. This time interval, T , is called the period.
A periodic function is a function for which a specific horizontal shift, P, results in the original function: f ( x + P ) = f ( x ) for all values of x. When this occurs we call the smallest such horizontal shift with P > 0 the period of the function.
The rotation rate of 1 revolution every 2 minutes is an angular velocity. We can use this rate to find a formula for the angle as a function of time. Since the point rotates 1 revolution = 2π radians every 2 minutes, it rotates π radians every minute. After t minutes, it will have rotated: ( t ) t radians.
Circular Motion: Period, Frequency, and Speed. Remember: Frequency (f) can have units of Hertz (1 rev/second), revolutions per unit time, or rotations per unit time. Ex: 4 revolutions per minute, 8 Hz, 6 rotations per second Period (T) will always have a unit of time. Ex: 3 s, 10 min.
I. Convert everything to sin and cos. Look for common pieces of trigonometric identities for clues as to how to proceed. Many solutions are possible.
The value of n can be calculated by examining the period of the function. \[\frac{2\pi}{n} = \text{period}\ \rightarrow n = \frac{2\pi}{\text{period}}\] The value of c will be the value of the y-intercept of the centreline (the horizontal line which lies in between the peaks and troughs).
Period, \(T\), is defined as the amount of time it takes to go around once - the time to cover an angle of \(2\pi\) radians. Frequency, \(f\), is defined as the rate of rotation, or the number of rotations in some unit of time. Angular frequency, \(\omega\), is the rotation rate measured in radians.
