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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.
circular motion. Special cases often dominate our study of physics, and circular motion about a central point is certainly no exception. There are many instances of central motion about a point; a bicycle rider on a circular track, a ball spun around by a string, and the rotation of a spinning wheel are just a few examples.
Because the speed v = r ω 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. In one period the object travels a distance s = vT equal to the circumference, = 2πr ; thus.
Period, $T$: The period is the time taken for one complete rotation. Since the Ferris wheel completes 3 rotations in 90 seconds, the time for one rotation is $90 \div 3 = 30$ seconds. So, $T = 30$ seconds. Frequency, $f$: The frequency is the number of rotations per second, which can be calculated as $f = \frac{1}{T} = \frac{1}{30} = 0.0333 ...
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.
Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. For example, any point on a propeller spinning at a constant rate is executing uniform circular motion. Other examples are the second, minute, and hour hands of a watch.
In the section on uniform circular motion, we discussed motion in a circle at constant speed and, therefore, constant angular velocity. However, there are times when angular velocity is not constant—rotational motion can speed up, slow down, or reverse directions.
