Question

The earth rotates ONCE in about 24 hour. Calculate its rotation frequency and its angular frequency.

Answer 1

Answer on Question #45505, Physics, Mechanics | Kinematics | Dynamics

Question:

The earth rotates ONCE in about 24 hour. Calculate its rotation frequency and its angular frequency.

Answer:

Rotational frequency (f) gives the number of rotations that an object undergoes in a specified unit of time. The period (T) is the time it takes the object to make one full rotation. Therefore:

$$f = \frac {1}{T} = \frac {1}{24 \cdot 60 \cdot 60 \ s} = 1.16 \cdot 10^{-5} \ Hz$$

One revolution is equal to $2\pi$ radians, hence

$$\omega = \frac {2 \pi}{T}$$

where $\omega$ is angular frequency, $T$ is time of 1 rotation.

$$\omega = \frac {2 \pi}{T} = \frac {2 \cdot 3.14}{24 \cdot 60 \cdot 60} = 7.27 \ \frac {\mathrm{rad}}{\mathrm{s}}$$

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