Question

Assuming the orbital radius of the Moon is 3.85 x 108 m, find the linear speed of the moon.

Answer 1

Answer:

1037 m/s

Explanation:

The linear speed of an object in circular motion is given by:

$v=\omega r$

where

$\omega$ is the angular velocity

r is the orbital radius

For the Moon, we know that

$r=3.85\cdot 10^8 m$ is the orbital radius

While we know also its orbital period:

$T=27 days \cdot (24\cdot 3600)=2.33\cdot 10^6 s$

So its angular velocity is

$\omega = \frac{2\pi}{T}=\frac{2\pi}{2.33\cdot 10^6}=2.69\cdot 10^{-6} rad/s$

And therefore, the linear speed is

$v=\omega r=(2.69\cdot 10^{-6})(3.85\cdot 10^8)=1037 m/s$