What Is the New Rotation Period for Zero Apparent Weight at the Equator?

AI Thread Summary
To achieve zero apparent weight at the equator of a planet with a radius of 4.4 million meters and a surface gravity of 10 m/s², the rotational speed must be increased. The concept of zero apparent weight means that the normal force acting on an object becomes zero, which occurs when the centrifugal force equals gravitational force. To find the new rotation period, one must apply Newton's second law and set the normal force to zero. The initial velocity calculated is 6633.25 m/s, but further calculations are needed to determine the new period and the factor by which the speed increases. Understanding the relationship between gravitational and centrifugal forces is crucial for solving this problem.
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Homework Statement


A planet similar to the Earth has a radius 4.4*10^6m and has an acceleration of gravity of 10 m/s^2 on the planet's surface.The planet rotates about its axis with a period of 25h. Imagine that the rotational speed can be increased.
a/If an object at the equator is to have zero apparent weight, what is the new period?
b/By what factor would the speed of the object be increased when the planet is rotating at the higher speed?


Homework Equations





The Attempt at a Solution



I found the Velocity of the planet = 6633.25, but then i don't know what do to next. I don't understand what does " obj. has zero apparent weight" mean?
b/ i have no idea about it...
 
Physics news on Phys.org
Regarding "zero apparent weight": Imagine you are standing on a scale. What the scale is actually reading is not your weight, but rather the normal force exerted on you by the scale. Draw a free body diagram and set up Newton's second law, and then ask yourself under what condition would that normal force drop to zero.
 

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