The earth has a radius of 6380 km and turns around once on its axis in 24 h. What is the radial acceleration of an object at the earth's equator? Give your answer in m/s² and as a fraction of g.

검증된 단계별 안내

First, convert the radius of the Earth from kilometers to meters. Since 1 km = 1000 m, the radius in meters is 6380 km * 1000 m/km = 6380000 m.

Next, calculate the angular velocity (ω) of the Earth. The Earth completes one full rotation in 24 hours, which is equivalent to 24 * 3600 seconds. The angular velocity is given by ω = 2π / T, where T is the period of rotation. So, ω = 2π / (24 * 3600) s.

The radial (centripetal) acceleration (a_r) at the Earth's equator can be calculated using the formula a_r = ω² * r, where r is the radius of the Earth. Substitute the values of ω and r to find a_r.

To express the radial acceleration as a fraction of g (acceleration due to gravity), use the value g = 9.81 m/s². Calculate the fraction by dividing the radial acceleration by g: fraction = a_r / g.

Ensure the units are consistent and check the calculations for accuracy. The final result will give you the radial acceleration in m/s² and as a fraction of g.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Centripetal Acceleration

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle. It is calculated using the formula a_c = v^2/r, where v is the tangential velocity and r is the radius of the circular path. This concept is crucial for determining the radial acceleration of an object at the Earth's equator.

Tangential Velocity

Tangential velocity refers to the linear speed of an object moving along a circular path. It is given by the formula v = 2πr/T, where r is the radius of the circle and T is the period of rotation. For the Earth, this period is 24 hours, and understanding this concept helps in calculating the centripetal acceleration at the equator.

Gravitational Acceleration (g)

Gravitational acceleration, denoted as g, is the acceleration due to Earth's gravity, approximately 9.81 m/s². When calculating the radial acceleration as a fraction of g, it provides a comparative measure of how the centripetal acceleration at the equator relates to the standard gravitational pull experienced by objects on Earth's surface.