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Ch 03: Motion in Two or Three Dimensions
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 03: Motion in Two or Three DimensionsProblema 25a
Capitolo 3, Problema 25a

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.

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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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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.
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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.
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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.
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