Assume that the standard kilogram would weigh exactly 9.80 N at sea level on the equator if the

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Assume that the standard kilogram would weigh exactly 9.80...

Assume that the standard kilogram would weigh exactly $9.80 \mathrm{~N}$ at sea level on the equator if the Earth did not rotate. Then take into account the fact that the Earth does rotate, so that this object moves in a circle of radius $6370 \mathrm{~km}$ (the Earth's radius) in one day. (a) Determine the centripetal force needed to keep the standard kilogram moving in its circular path. ( $b$ ) Find the force exerted by the standard kilogram on a spring balance from which it is suspended at the equator (its apparent weight).

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Key Concepts

Centripetal Force

Centripetal force is the net force required to keep an object moving in a circular path. It is directed towards the center of the circle and is calculated using the relationship F = m(v^2/r) or F = m(4?^2r/T^2), where m is the mass, r is the radius of the circular path, v is the tangential speed, and T is the period of rotation. This concept is essential when analyzing the dynamics of bodies in circular motion, such as objects on Earth's rotating surface.

Apparent Weight in a Rotating System

Apparent weight is the reading given by a measuring device like a spring balance, which reflects the net force acting on an object in a non-inertial, rotating frame. In the case of a body at the Earth's equator, the apparent weight is the result of the gravitational force acting downward less the centripetal force required to sustain the circular motion due to the Earth's rotation. This adjusted force gives insight into the effective acceleration acting on the object, differing slightly from the standard gravitational acceleration.

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