Question

the angular speed of a point on a planet is $\frac{5pi}{14}$ radian per hour. the equator lies on a circle of radius approximately 8000 miles. find the linear velocity, in miles per hour, of a point on the equator.
the linear speed of a point on the equator is approximately $square$ miles per hour
(round to the nearest whole number as needed.)

Explanation:

Step1: Recall the linear - velocity formula

The formula for linear velocity $v$ in terms of angular velocity $\omega$ and radius $r$ is $v = r\omega$.

Step2: Identify the values of $r$ and $\omega$

We are given that $r = 8000$ miles and $\omega=\frac{5\pi}{14}$ radians per hour.

Step3: Substitute the values into the formula

$v=8000\times\frac{5\pi}{14}=\frac{40000\pi}{14}=\frac{20000\pi}{7}$.

Step4: Calculate the numerical value

$v=\frac{20000\pi}{7}\approx\frac{20000\times 3.14159}{7}\approx\frac{62831.8}{7}\approx8976$.

Answer:

$8976$