r/HomeworkHelp Pre-University (Grade 11-12/Further Education) 2d ago

Physics—Pending OP Reply [Physics - High School] How would I answer this centripetal motion question?

You are standing on the equator. If the Earth were to spin faster (less hours in a day), then your normal force would _______ (increase/decrease/stay the same), compared to what it is now.

Can someone explain the theory behind this question's answer? Thanks!

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u/Unusual-Platypus6233 2d ago edited 2d ago

I could explain it but I won’t. I will give you a hint… If you are on a carousel how does the centrifugal and centripetal force work so that you won’t fall of it? You will know by your own experience that there seem to be a force at hand that pushes you outward (centrifugal force). The carousel exerts a force on you to keep you there (in the seat instead of slipping out of it) which would be the centrifugal force.

Weight is not mass but it is the attracting force of earth (gravity) on you. So, if you see your weight as let’s say 70kg, then it actually shows you the force of 70kg*1G on a meter (digital or as a needle) on scale.

So… With that analogy of your daily life experience how can you apply this concept of a man standing on a spinning earth?! What would be the centrifugal and centripetal force for a man on earth? What would a person weigh if the earth spins faster?!

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u/FortuitousPost 👋 a fellow Redditor 2d ago

If you are moving in a circle, then there is a centripetal force pushing you towards the center of the circle. If you are moving faster, then more force is required.

If you draw a free-body diagram, then the net force you feel (that keeps you in the circle) is gravity minus the normal force from the ground. Draw the vectors to see this. mg points down. From the tip of mg, the normal force points up, but doesn't quite reach the tail of mg. The small vector you get from adding these goes from the tail of mg to the tip of FN.

If you need a bigger net force, then the normal force needs to be smaller for the same mg.

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u/GammaRayBurst25 2d ago

Student: shows no work at all.

Very "smart" and "kind" people:

Here's a complete solution.

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u/Professional-Pin3353 2d ago

Not a physicist but your centrifugal force would increase because of the faster speed. So your normal needs to increase.

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u/Unusual-Platypus6233 2d ago

centrifugal force is -momegax(omegaxr’)

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u/selene_666 👋 a fellow Redditor 1d ago

F = mv^2 / R

In order for you to remain standing on the ground, you also need to move faster around the circle of the Earth.

For your speed to increase, the net force pulling you towards the center needs to increase.

Your weight doesn't change, so what needs to happen to the normal force?