The earth spins on its axis once every 24 hours and its radius is 3960 miles. Find the angular speed in radians/hour and the linear speed in miles/hour of a point on the equator.
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
![The Earth spins on its axis once every 24 hours and its radius is 3960 miles. Find the angular speed in radians/hour and the linear speed in miles/hour of a point on the equator.
---
**Explanation:**
To find the angular speed in radians per hour, we use the formula for angular speed, \(\omega\), which is given by:
\[
\omega = \frac{\theta}{t}
\]
where \(\theta\) is the angle in radians and \(t\) is the time in hours. Since the Earth completes one full rotation (2π radians) in 24 hours:
\[
\omega = \frac{2\pi}{24} = \frac{\pi}{12} \, \text{radians/hour}
\]
To find the linear speed, \(v\), of a point on the equator, we use the formula:
\[
v = r \cdot \omega
\]
where \(r\) is the radius of the Earth:
\[
v = 3960 \cdot \frac{\pi}{12}
\]
Simplifying gives:
\[
v = 330\pi \, \text{miles/hour}
\]
This formula provides the speed at any point along the equator, where the Earth’s rotational effects are most straightforwardly felt.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5750978-55c7-40b5-89f2-af55175d1340%2F03a1933c-a216-4b35-b40e-fa3bdd3d7050%2Fuhnmt8_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
