The earth has a radius of 6380 km and turns around once on its axis in 24 h.

1)What is the radial acceleration of an object at the earth's equator? Give your answer in m/s^2

2) What is the radial acceleration of an object at the earth's equator? Give your answer as a fraction of g.

3) If a_rad at the equator is greater than g , objects would fly off the earth's surface and into space. What would the period of the earth's rotation have to be for this to occur?

9.78

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To find the answers to these questions, we need to make use of the formulas for radial acceleration and centripetal acceleration.

1) Radial acceleration (a_rad) is given by the formula:
a_rad = r * ω^2
where r is the radius and ω is the angular velocity.

Given:
Radius of the Earth, r = 6380 km = 6380 * 1000 m (converting km to meters),
Angular velocity, ω = 2π / T, where T is the period (time taken for one complete rotation).

To find a_rad, we need to find the value of ω. We know that the Earth completes one rotation in 24 hours (or 24 * 3600 seconds).
So, T = 24 * 3600 seconds.

Substituting the values into the equation:
a_rad = 6380 * 1000 * (2π / (24 * 3600))^2

Calculating this will give us the radial acceleration in m/s^2.

2) To find the radial acceleration as a fraction of g, we can divide a_rad by the acceleration due to gravity (g = 9.8 m/s^2).

So, radial acceleration as a fraction of g = a_rad / g.
This calculation will give us the ratio of a_rad to g.

3) If a_rad at the equator is greater than g, objects would fly off the Earth's surface. In other words, a_rad > g.

To find the period of rotation necessary for this to occur, we rearrange the previous formula for a_rad:
a_rad = r * ω^2
ω = sqrt(a_rad / r)

Substituting the values of a_rad and r, we can solve for ω. Once we have the value of ω, we can calculate the period (T) using the equation ω = 2π / T.

SUCK MAH WIGGILY DEEK

1) acceleration = r w^2

where w is the angular velocity in radians per second
w = 2 pi/(24*3600)
r = 6380 km

2) Divided the acceleration by 9.8 m/s^2 per g

3) Solve g = r w^2 for the w value that lets objects fly off the earth.

Honor the hindus

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