Weight before/after change in rotation Speed

In summary, the weight of a person in a location at 48 North and 123 West would decrease if the rotation rate increased to make a day 3 hours long. This is due to the addition of the centrifugal force, a fictitious force that is needed to balance out the sum of forces on the person in the rotating frame of the Earth. The Coriolis force, which is tangent to the Earth's surface, is also needed to calculate the component of the centrifugal force normal to the surface of the Earth.
  • #1
Charanjit
48
0

Homework Statement



How would the weight of a person in some place (48 North and 123 West) change if the rotation rate increased so a day was 3 hours long?


Homework Equations



F=ma

The Attempt at a Solution



The above is not the only equation I think that is needed for this. Not sure about this, but coriolis force maybe needed. I just have no clue about this.
 
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  • #2
Sum of forces on the person = 0 since he's not going anywhere (hint: there are 3 terms in the equation, and yes, it's basically F = ma, except if you're going to derive evbrything you need from that one equation, remember that F and a are vectors, not just scalars).
 
  • #3
Yes, I understand that F=ma = 0 since the person will not move. Now the three terms that come into play... would the centrifugal force help at all since the Earth is rotating?
 
  • #4
Yes it would. Since gravitational attrcation is constant, irrespective of rotational speed, what force do you think has to change so the three add up to zero?
 
  • #5
You are working in a frame fixed to the Earth which is a rotating object hence you are in a rotating frame. Which means that you need to use fictious forces. You need the centrifugal force. The coriolis force is tangent to the Earth's surface... Calculate the component of the centrifugal force normal to the surface of the earth...
 

What is the relationship between weight and change in rotation speed?

The relationship between weight and change in rotation speed is known as the moment of inertia. The moment of inertia is a measure of an object's resistance to changes in its rotation speed. The greater the weight of an object, the greater its moment of inertia and therefore the more force is required to change its rotation speed.

How does weight affect the stability of an object during rotation?

Weight plays a major role in the stability of an object during rotation. A heavier object will have a larger moment of inertia, making it more difficult to change its rotation speed. This increased resistance to change in rotation speed results in greater stability for the object.

Does changing the weight of an object impact its rotation speed?

Yes, changing the weight of an object will impact its rotation speed. Objects with a larger moment of inertia, such as heavier objects, require more force to change their rotation speed. Therefore, increasing or decreasing the weight of an object will affect its rotation speed.

How can I calculate the change in rotation speed of an object based on its weight?

To calculate the change in rotation speed of an object based on its weight, you will need to know the moment of inertia of the object and the amount of force applied to it. The equation for calculating the change in rotation speed is Change in Rotation Speed = Force / Moment of Inertia. This means that the larger the moment of inertia, the smaller the change in rotation speed will be for a given force.

What are some real-world applications of understanding the relationship between weight and change in rotation speed?

Understanding the relationship between weight and change in rotation speed has many practical applications. For example, engineers and designers use this knowledge to create stable structures and vehicles, such as bridges and airplanes, that can withstand the forces of rotation. It is also important in sports, such as figure skating and gymnastics, where athletes must control their weight and rotation speed to perform complex movements. Additionally, understanding this relationship is crucial in space exploration, as it allows scientists to calculate the necessary force and speed needed for objects to rotate and orbit in space.

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