The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. assuming the earth is a sphere with a radius of 6.38 × 106 m, determine the speed and centripetal acceleration of a person situated (a) at the equator and (b) at a latitude of 30.0° north of the equator.

Answer

given,

Radius of earth = 6.38 x 10⁶ m

angular velocity  =

                            =

                            =

a) at equator

velocity v   = R ω  = 6.38 x 10⁶ x 7.27 x 10⁻⁵

             v = 463.8 m/s

centripetal acceleration = R ω² = 6.38 x 10⁶ x (7.27 x 10⁻⁵)²

                                        = 0.0337 m/s²

b) at a latitude of 30.0° north of the equator

r = R cos θ  =  6.38 x 10⁶ cos 30⁰ =  3.19 x  10⁶ m

velocity v   = R ω  = 3.19 x  10⁶ x 7.27 x 10⁻⁵

            v = 231.9 m/s

centripetal acceleration = R ω² = 3.19 x  10⁶  x (7.27 x 10⁻⁵)²

                                        = 0.0168 m/s²

answer would be letter choice (a),   a ball resting on a shelf. would be another example of potential energy   >   stored energy > not moving.

a ball spinning on a finger   >   kinetic energy > moving energy

a ball rolling on the ground   >   kinetic energy   > moving energy

a   ball flying through the air   > kinetic energy   >   moving energy

hope that                                         : )