(a) The Earth completes one rotation every 24 hours. To find the angular velocity, we need to convert this time period into seconds and then calculate the angular velocity using the formula:

Angular velocity (ω) = 2π / T

where T is the period of rotation.

First, convert 24 hours into seconds:

24 hours = 24 * 60 * 60 = 86400 seconds

Then, substitute this value into the formula:

ω = 2π / 86400 ≈ 7.27 x 10^-5 rad/sec

(b) The moment of inertia (I) of a solid sphere, like the Earth, is given by the formula:

I = 2/5 * m * r^2

where m is the mass of the Earth and r is its radius.

Substitute the given values into the formula:

I = 2/5 * 5.98 x 10^24 kg * (6.37 x 10^6 m)^2 ≈ 9.7 x 10^37 kg*m^2

So, the Earth's moment of inertia is approximately 9.7 x 10^37 kg*m^2.

Question

(a) The Earth completes one rotation every 24 hours. To find the angular velocity, we need to convert this time period into seconds and then calculate the angular velocity using the formula:

Angular velocity (ω) = 2π / T

where T is the period of rotation.

First, convert 24 hours into seconds:

24 hours = 24 * 60 * 60 = 86400 seconds

Then, substitute this value into the formula:

ω = 2π / 86400 ≈ 7.27 x 10^-5 rad/sec

(b) The moment of inertia (I) of a solid sphere, like the Earth, is given by the formula:

I = 2/5 * m * r^2

where m is the mass of the Earth and r is its radius.

Substitute the given values into the formula:

I = 2/5 * 5.98 x 10^24 kg * (6.37 x 10^6 m)^2 ≈ 9.7 x 10^37 kg*m^2

So, the Earth's moment of inertia is approximately 9.7 x 10^37 kg*m^2.

Knowee AI · Accepted Answer