What is the value of the angular velocity of a point on the surface of the Earth?
A 1.2 × 10–5
 rad s–1
B 7.3 × 10–5
 rad s–1
C 2.6 × 10–1
 rad s–1
D 4.6 × 102
 rad s–1

The angular velocity (\(\omega\)) of a point on the surface of the Earth is related to the time it takes for the Earth to complete one full rotation (a day, which is approximately 24 hours). We can calculate the angular velocity using the following formula:

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

where:
- \(T\) is the time period of one full rotation of the Earth, which is 24 hours or 86400 seconds.

Let's compute it:

\[
\omega = \frac{2\pi}{86400 \, \text{seconds}} \approx 7.27 \times 10^{-5} \, \text{rad/s}
\]

Therefore, the angular velocity of a point on the Earth's surface is approximately **\(7.3 \times 10^{-5} \, \text{rad/s}\)**, which corresponds to option **B**.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the significance of angular velocity in planetary motion?
2. How does the Earth's rotation affect time zones?
3. What would happen if the Earth's angular velocity increased?
4. How does angular velocity differ between the Earth's rotation and its orbit around the Sun?
5. How does angular velocity relate to centrifugal force on the Earth's surface?

**Tip:** Angular velocity is a measure of how fast an object rotates or revolves relative to another point, often expressed in radians per second.

What is the value of the angular velocity of a point on the surface of the Earth?
A 1.2 × 10–5 rad/s
B 7.3 × 10–5 rad/s
C 2.6 × 10–1 rad/s
D 4.6 × 102 rad/s

Explore how to calculate the angular velocity of a point on Earth's surface using the rotational period of the Earth. The solution applies the formula ω = 2π / T, resulting in an angular velocity of approximately 7.3 × 10^-5 rad/s. Suitable for Grades 9-12 students learning about rotational motion and angular velocity.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation