Question

Calculate the angular velocity of the earth in its orbit around the sun.

Answer 1

Answer:

$0.0172rad/day=1.99x10^{-7}rad/second$

Explanation:

The definition of angular velocity is as follows:

$\omega=2\pi f$

where $\omega$ is the angular velocity, and $f$ is the frequency.

Frequency can also be represented as:

$f=\frac{1}{T}$

where $T$ is the period, (the time it takes to conclude a cycle)

with this, the angular velocity is:

$\omega=\frac{2\pi}{T}$

The period T of rotation around the sun 365 days, thus, the angular velocity:

$\omega=\frac{2\pi}{365days}=0.0172rad/day$

if we want the angular velocity in rad/second, we need to convert the 365 days to seconds:

Firt conveting to hous

$365days(\frac{24hours}{1day} )=8760hours$

then to minutes

$8760hours(\frac{60minutes}{1hour} )=525,600minutes$

and finally to seconds

$525,600minutes(\frac{60seconds}{1minute})=31,536x10^3seconds$

thus, angular velocity in rad/second is:

$\omega=\frac{2\pi}{31,536x10^3seconds}=1.99x10^{-7}rad/second$