Question

The earth's radius is 6.37×106m; it rotates once every 24 hours. you may want to review ( pages 195 - 198) . part a what is the earth's angular speed

Answer 1

The angular speed of Earth is $\fbox{\begin\\\ \bf 7.268\times 10^{-5}\ \text{radian per second}\\\end{minispace}}$.

Further explanation:

It is given that the radius of Earth is $6.37\times10^{6}\ \text{meters}$ and it rotates once in every  $24$ hours.

The angular speed of earth is nearly constant and Earth takes one day to complete one rotation that means the time interval for earth to complete one revolution is $1\ \text{day}$.

The total angular displacement covered by the earth to complete one revolution is $2\pi\text{radian}$.

One day is equivalent to $24\ \text{hours}$, $1\ \text{hour}$ is equivalent to $60\ \text{minutes}$ and $1\ \text{minute}$ is equivalent to $60\ \text{seconds}$.

The total number of seconds in $1\ \text{day}$ is calculated as follows:

$\fbox{\begin\\\ \begin{aligned}1\ \text{day}&=24\ \text{hours}\\&=24\times60\ \text{minutes}\\&=1440\ \text{minutes}\\&=1440\times60\ \text{seconds}\\&=86400\ \text{seconds}\end{aligned}\\\end{minispace}}$    

Therefore the time taken to complete one revolution is $86400\ \text{seconds}$.

The angular velocity is defined as the rate of change of angular displacement. So the formula for angular velocity is, as follows:

$\fbox{\begin\\\ \omega=\dfrac{\theta}{t}\\\end{minispace}}$

In the above equation $\omega$ represents angular velocity, $\theta$ represents angular displacement and $t$ represents time.

To obtain the value of angular velocity of Earth substitute $2\pi$ for $\theta$ and $86400$  for $t$ in the above equation.

$\begin{aligned}\omega&=\dfrac{2\pi}{86400}\\&=\dfrac{2\times3.14}{86400}\\&=\dfrac{6.28}{86400}\\&=7.268\times10^{-5}\end{aligned}$

Therefore, the value of $\omega$ is $7.268\times10^{-5}$.

Thus, the angular speed of the Earth is $\fbox{\begin\\\ \bf 7.268\times 10^{-5}\ \text{radian per second}\\\end{minispace}}$.

Learn more:

1. Problem on the magnitude of acceleration: brainly.com/question/1597065
2. Problem on simplification: brainly.com/question/1602237
3. Problem on general form of given circle: brainly.com/question/1506955

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Angular motion

Keyword: Angular velocity, angular displacement, time, one revolution, radian/second, Earth, 86400 seconds, 2pi, speed, minutes, omega, theta.

Answer 2

See attached formula and Answer: