Assume that the earth is a sphere of radius 3960 miles. How fast (in miles per hour)
is a point on the equator moving as a result of the earth’s rotation about its axis?

To determine the speed at which a point on the equator is moving due to the Earth's rotation, we can follow these steps:

### Step 1: Determine the Circumference of the Earth
The Earth is assumed to be a sphere, so the circumference \( C \) at the equator can be calculated using the formula:

\[
C = 2\pi r
\]

where \( r = 3960 \) miles is the radius of the Earth.

\[
C = 2 \times \pi \times 3960 \approx 2 \times 3.1416 \times 3960 \approx 24,881.52 \text{ miles}
\]

### Step 2: Determine the Rotational Speed
The Earth completes one full rotation every 24 hours. Therefore, the speed \( v \) of a point on the equator is given by the distance traveled (the circumference) divided by the time taken (24 hours):

\[
v = \frac{C}{T} = \frac{24,881.52 \text{ miles}}{24 \text{ hours}} \approx 1,036.73 \text{ miles per hour}
\]

### Final Answer
A point on the equator is moving at approximately **1,036.73 miles per hour** as a result of the Earth's rotation.

Would you like details or have any questions?

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Here are 5 related questions:

1. How does the rotational speed change as you move towards the poles?
2. What is the rotational speed at a latitude of 45 degrees?
3. How would the speed change if the Earth's radius were larger or smaller?
4. How does the rotational speed affect the Earth's shape?
5. What is the relationship between rotational speed and centrifugal force?

**Tip:** Understanding the Earth's rotational speed can help explain various phenomena like the Coriolis effect, which influences weather patterns.

Discover how fast a point on the equator moves due to Earth's rotation with our detailed calculation. Understand the circumference formula and speed formula used to determine the speed of rotation. Approximate speed: 1,036.73 miles per hour. Suitable for Grades 9-12.

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