If the length of the Equator is about 40000 km and the velocity of rotation is about 1700 km per hour, what would be the velocity of rotation at the Pole?

Options

A. Zero
B. 850 km/hr
C. 1700 km/hr
D. 3400 km/hr

Explanation

To find the velocity of rotation at the poles, we can follow these steps:

### Step 1: Understand the Concept of Linear Velocity
The linear velocity (v) at any point on the Earth's surface due to its rotation is given by the formula:
\[ v = r \cdot \omega \cdot \sin(\theta) \]
where:
- \( r \) is the radius of the Earth,
- \( \omega \) is the angular velocity of the Earth,
- \( \theta \) is the angle from the equator.

### Step 2: Determine the Radius of the Earth
From the problem, we know that the length of the equator is approximately 40,000 km. The radius \( r \) can be calculated as:
\[ r = \frac{\text{Circumference}}{2\pi} \]
However, since we are given the linear velocity at the equator, we can directly use that information without calculating the radius explicitly.

### Step 3: Identify the Angular Velocity
The angular velocity \( \omega \) can be derived from the linear velocity at the equator:
\[ v_{\text{equator}} = r \cdot \omega \]
Given that the linear velocity at the equator is 1700 km/h, we can express \( \omega \) as:
\[ \omega = \frac{v_{\text{equator}}}{r} \]

### Step 4: Analyze the Situation at the Poles
At the poles, the angle \( \theta \) is either 0 degrees (North Pole) or 180 degrees (South Pole). Therefore, we can substitute \( \theta \) into the formula:
- For the North Pole: \( \sin(0) = 0 \)
- For the South Pole: \( \sin(180) = 0 \)

### Step 5: Calculate the Velocity at the Poles
Using the formula:
\[ v_{\text{pole}} = r \cdot \omega \cdot \sin(\theta) \]
Since \( \sin(0) = 0 \) and \( \sin(180) = 0 \), we find:
\[ v_{\text{pole}} = r \cdot \omega \cdot 0 = 0 \]

### Conclusion
Thus, the velocity of rotation at the poles is:
\[ v_{\text{pole}} = 0 \text{ km/h} \]

### Summary
The velocity of rotation at the poles is 0 km/h because the sine of the angle at the poles (0 or 180 degrees) is zero.

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