Respuesta :
Answer:
[tex]0.0172rad/day=1.99x10^{-7}rad/second[/tex]
Explanation:
The definition of angular velocity is as follows:
[tex]\omega=2\pi f[/tex]
where [tex]\omega[/tex] is the angular velocity, and [tex]f[/tex] is the frequency.
Frequency can also be represented as:
[tex]f=\frac{1}{T}[/tex]
where [tex]T[/tex] is the period, (the time it takes to conclude a cycle)
with this, the angular velocity is:
[tex]\omega=\frac{2\pi}{T}[/tex]
The period T of rotation around the sun 365 days, thus, the angular velocity:
[tex]\omega=\frac{2\pi}{365days}=0.0172rad/day[/tex]
if we want the angular velocity in rad/second, we need to convert the 365 days to seconds:
Firt conveting to hous
[tex]365days(\frac{24hours}{1day} )=8760hours[/tex]
then to minutes
[tex]8760hours(\frac{60minutes}{1hour} )=525,600minutes[/tex]
and finally to seconds
[tex]525,600minutes(\frac{60seconds}{1minute})=31,536x10^3seconds[/tex]
thus, angular velocity in rad/second is:
[tex]\omega=\frac{2\pi}{31,536x10^3seconds}=1.99x10^{-7}rad/second[/tex]
