Answer: T = 5068 s
Explanation:
Given
Radius of the earth, r = 6378.1 km
Centripetal acceleration, g = 9.81 m/s²
Period of rotation, T = ?
a = w²r, where
a is the centripetal acceleration
w is the angular velocity
r is the radius
9.81 = w² * 6378.1*10^3
w² = 9.81 / 6378.1*10^3
w² = 1.538*10^-6
w = 1.24*10^-3 rad/s
To get the period of the earth, we use the formula
w = 2π / T, so that
T = 2π / w
T = (2 * 3.142) / 1.24*10^-3
T = 6.284 / 1.24*10^-3
T = 5067.74 s
Therefore, the earth would rotate at a period of 5068 s or 1 hour and 24 minutes
Answer:
The time period of Earth’s rotation would be 84.4 minutes
Explanation:
Given that,
Centripetal acceleration = 9.81 m/s²
Radius ,r = 6378.1 km
Velocity, v
Centripetal acceleration is
[tex]a_c=\dfrac{v^2}{r}[/tex]
[tex]a_c=\dfrac{v^2}{r}\\\\\Rightarrow v=\sqrt{a_cr}\\\\\Rightarrow v=\sqrt{9.81\times 6378100}\\\\\Rightarrow v=7910.067\ m/s[/tex]
Time period is given by
[tex]T=\dfrac{2\times \pi \times r}{v\times 60}\\\\ T=\dfrac{2\times \pi \times 6378.1\times 10^3}{7910.06706\times 60}\\\\ T=84.4\ minutes[/tex]
Hence, the time period of Earth’s rotation would be 84.4 minutes
