A spherically planet (for example the earth) has a radius R, mass M, and rotates

Question

A spherically planet (for example the earth) has a radius R, mass M, and rotates with an angular velocity vector ? about an axis through its center. (a) Consider a motion of a particle of (constant) mass m close to the surface of the planet. Derive the equation of motion relative to a frame ? fixed on the planet's surface (known as a laboratory frame) based on the approximation that the cen- trifugal and gravitational forces are constant and can be combined in an effective gravitational force. (5 pts) Hint: Consider that ? is placed at a latitude ? (b) Evaluate and analyze the effective gravitational acceleration. (3 pts)

Explanation / Answer

(b) * The study of the motion of the simple pendulum provided valuable insights into the gravitational force acting on the students at the University of Utah.

The experiment was of value since the gravitational force is one all people continuously experience and the collection and analysis of data proved to be a rewarding learning experience in error analysis. Furthermore, this experiment tested a mathematical model for the value of gravity that that makes use of the small-angle approximation and the proportional relationship between the square of the period of oscillations to the length of the pendulum.Sources of error for this procedure included precision in both length and time measurement tools, reaction time of the stopwatch holder, and the accuracy of the stopwatch with respect to the lab atomic clock. The final result of g takes into account the correction for the error introduced using the approximation.

There are opportunities to correct for the effects of mass distribution, air buoyancy and damping, and string stretching.

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