Respuesta :
Answer:
Given that
The earth spins on its axis once a day and orbits the sun once a year (365 1/4 days)
a)
When earth spins on its axis
We know that earth take 1 day to complete one revolution around its own axis.
T= 1 day = 24 hr = 24 x 3600 s
T=86400 s
We know that
T=2π/ω
ω= 2π/T
ω= 2π/86400
ω=7.27 x 10⁻5 rad/s
b)
When earth revolve around earth
T =365 1/4 days = 365.25 days
T= 365.24 x 86400 s
T=31557600
We know that
T=2π/ω
ω= 2π/T
ω= 2π/31557600
ω=1.99 x 10⁻⁷ rad/s
Answer:
(a) [tex]7.27\times 10^{- 5}\ rad/s[/tex]
(b) [tex]1.99\times 10^{- 7}\ rad/s[/tex]
Solution:
As per the question:
The time period of the Earth's spin on its axis, T = 1 day
1 day = [tex]24\times 60\times 60 = 86400\ s[/tex]
Now,
(a) The Earth's average angular velocity is given by:
[tex]\omega = \frac{2\pi}{T}[/tex]
[tex]\omega = \frac{2\pi}{86400} = 7.27\times 10^{- 5}\ rad/s[/tex]
(b) Time period for orbiting the sun, T':
T' = [tex]365 \frac{1}{4} = 365.25\ days[/tex]
T' = [tex]365.25\times 24\times 60\times 60 = 3.1557\times 10^{7}\ s[/tex]
Angular velocity, [tex]\omega'[/tex]:
[tex]\omega' = \frac{2\pi}{T'} = \frac{2\pi}{3.1557\times 10^{7}} = 1.99\times 10^{- 7}\ rad/s[/tex]
