Earth rotates on its axis once every 24 hours, so that objects on its surface execute uniform circular motion about the axis with a period of 24 hours. consider only the effect of this rotation on the person on the surface. (ignore earth's orbital motion about the ) what is the speed and what is the magnitude of the acceleration of a person standing on the equator? express the magnitude of this acceleration as a percentage of g.(b) what is the direction of the acceleration vector? (c) what is the speed and what is the magnitude of the acceleration of a person standing on the surface at 35â°n latitude? (d) what is the angle between the direction of the acceleration of the person at 35â°n and the direction of the acceleration of the person at the equator if both persons are at the same longitude?

V = 4.63 10² m / s

 ac = 3.37 10⁻²  m/s²

Explanation:

This is a uniform circular motion, so we can calculate centripetal laceration of the object

       ac = v² / r

Where v is the speed of the object and r the radius of the Earth, 6.37 106 m.

a) The speed of the object can be calculated from the distance traveled in the time called period (T)

       V = d / t

       T = 24 h (3600 c / 1 h) = 86400 s

Circle length d = 2π r

      V = 2π 6.37 10⁶/86400

      V = 4.63 10² m / s

With this data we calculate the acceleration of the body

     ac = (4.63 10²)² / 6.37 10⁶

     ac = 3.37 10⁻²  m/s²

To express the acceleration as a percentage of the acceleration of gravity we divide the two magnitudes

      Fraction = ac / g

      Fraction = 3.37 10⁻⁻² / 9.8

      Fraction = 3.4 10⁻³

      ac = 3.4 10⁻³ g

b) The acceleration vector is directed to the center of the circle which, in this case, being in Ecuador coincides with the center of the Earth

c) In this case the person continues to perform a circular movement, in a constant time of 24 h, what has changed is that since we are on a sphere the circle radius for 35ºN is different from the radius of the Tiera.

Let's use some trigonometry

       sin 35 = r / R

Where r is the radius of the circle and R is the radius of the Earth

      r = R sin 35

       r = 6.37 10⁶ sin 35

     r = 3.65 10⁶ m

We calculate the speed and acceleration at this point

    v = 2π 3.65 10⁶/86400

    v = 2.65 10² m / s

   ac = (2.65 10²)² / 3.65 10⁶

   ac = 1.9 10⁻² m/s²

d) The centripetal acceleration of the person at 35º is directed to the center of the circle and the acceleration of the mass is directed to the center of the earth, in this has one of 35 below the horizontal.

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