The angular speed of earth around its own axis is

Options

A. `(pi)/(43200) `rad/s
B. `(pi)/(3600)`rad/s
C. `(pi)/(86400)` rad/s
D. `(pi)/(1800)`rad/s

Answer

To find the angular speed of the Earth around its own axis, we can follow these steps:

### Step 1: Understand the Concept of Angular Speed
Angular speed (ω) is defined as the rate of change of angular displacement with respect to time. It is usually measured in radians per second.

### Step 2: Identify the Time Period
The Earth completes one full rotation around its axis in 24 hours. We need to convert this time period into seconds for our calculations.

\[ \text{Time period (T)} = 24 \text{ hours} = 24 \times 60 \times 60 \text{ seconds} \]

### Step 3: Calculate the Time Period in Seconds
Now, we calculate the time period in seconds:

\[ T = 24 \times 60 \times 60 = 86400 \text{ seconds} \]

### Step 4: Use the Formula for Angular Speed
The formula for angular speed is given by:

\[ \omega = \frac{2\pi}{T} \]

### Step 5: Substitute the Time Period into the Formula
Now, we substitute the value of T into the formula:

\[ \omega = \frac{2\pi}{86400} \]

### Step 6: Calculate the Angular Speed
Now we can perform the calculation:

\[ \omega = \frac{2\pi}{86400} \approx \frac{6.2832}{86400} \approx 7.272 \times 10^{-5} \text{ radians per second} \]

### Final Answer
Thus, the angular speed of the Earth around its own axis is approximately:

\[ \omega \approx 7.272 \times 10^{-5} \text{ radians per second} \]

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