Question

How would you calculate the speed at which the moon revolves around the earth is m/s?

Answer 1

In order to calculate the speed of the moon we need two quantities

1. Distance of the moon from center of the earth
2. Total times taken by the moon revolving around the earth
   By using these two quantities we can calculate the speed of the moon.
   Formula used:
   $v=\dfrac{2\pi r}{T}$

Complete answer:
In order to calculate the speed of the moon we will use the below equation.
$v=r\omega .....\left( 1 \right)$
Where, v = velocity
r = orbital radius of the moon
$\omega$= angular velocity
Now we know that the angular velocity
$\omega =\dfrac{2\pi }{T}$
Now substitute value of $\omega$in the equation (1)
$v=\dfrac{2\pi \times r}{T}....\left( 2 \right)$
Where, T = orbital period
Now we know that moon is 384,000km away from the earth therefore,
r = 384,000km
Moon revolves around the earth in 27.3 days therefore,
T = 27.3 days
Now convert units from the days to second
$\begin{aligned} & \Rightarrow T=27.3\times 60\times 60\times 24 \\\ & =2,358,720S \\\ \end{aligned}$
Now substitute all the values in the equation (2)
$\begin{aligned} & v=\dfrac{2\pi \times 384000}{2,358,720} \\\ & =1.022km/s \\\ \end{aligned}$
Converting the unit from km/s to m/s
$\begin{aligned} & \Rightarrow v=1.022\times {{10}^{3}}m/s \\\ & \therefore v=1022m/s \\\ \end{aligned}$
Therefore speed of the moon that is revolving around the earth is 1022m/s

Note:
As an approach to solve this question we use this formula $v=\dfrac{2\pi r}{T}$ in which we put value of r as the distance between earth and the moon and T as revolving time of the moon around the earth.