Tangential velocity of the earth

In summary, the conversation discusses determining the speed at which the Earth would have to rotate on its axis in order for a person on the equator to weigh 3/4 of their original weight. The equations used include VT=r*ω and ƩF=M*ac=m*Vt^2/r, and the discussion also involves determining the normal force.
  • #1
RTW69
374
1

Homework Statement


Determine the speed with which the Earth would have to turn to rotate on its axis so that a person on the equator would weigh 3/4 as much


Homework Equations


VT=r*ω ; Vi=469 m/s is tangential velocity of earth

ƩF=M*ac=m*Vt^2/r



The Attempt at a Solution



The positive direction is toward the center of the earth.

From ƩF=m*ac

Initial: m*g-Ni=m*Vi^2/r

Final: 3/4m*g-Nf=m*Vf^2/r

Since m*g is the same for initial and final state I assume that Ni=Nf

Therefore:3/4m*g-[mg-m*Vi^2/r]=m*Vf^2/r or

Vf=Sqrt(Vi^2-r*g/4)

I have a sign error. I end up taking the square root of a negative number but the physics looks OK. Suggestions?
 
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  • #2
Nf is to be 3/4 of what? And what equation tells you what it will actually be? (Your 'Final' equation is completely wrong.)
 
  • #3
OK, Final:m*g-3/4*N=m*Vf^2/r
 
  • #4
Looks right, if N is what you wrote as Ni previously,
 
  • #5


I appreciate your attempt at finding a solution to this problem. However, I would like to clarify a few things. The tangential velocity of the Earth at the equator is not a constant value, as it varies with latitude due to the Earth's oblate shape. Additionally, the weight of an object is influenced by the gravitational force, which is dependent on the mass and distance of the object from the center of the Earth. Therefore, the weight of an object on the equator would not be affected solely by the Earth's rotation.

That being said, if we assume that the Earth's rotation is the only factor affecting weight, your approach using the equations of motion is correct. However, there may be a mistake in your calculations, which could be causing the sign error. I would suggest double-checking your calculations and units to ensure accuracy. Additionally, it may be helpful to consider the Earth's rotational speed at the equator, which is approximately 1670 km/h, and see how it compares to the value you have calculated.

In conclusion, while your approach is scientifically sound, it is important to consider all factors and double-check calculations to ensure accuracy. Keep up the good work!
 

Related to Tangential velocity of the earth

1. What is the tangential velocity of the earth?

The tangential velocity of the earth is the speed at which the earth is moving as it orbits around the sun. This velocity varies depending on the distance between the earth and the sun, but on average it is approximately 67,000 miles per hour.

2. How is the tangential velocity of the earth calculated?

The tangential velocity of the earth is calculated by dividing the distance traveled by the earth around the sun (its circumference) by the time it takes to complete one orbit (its period). This calculation is represented by the formula v = 2πr/T, where v is the tangential velocity, r is the distance from the earth to the sun, and T is the period of the earth's orbit.

3. How does the tangential velocity of the earth affect our daily lives?

The tangential velocity of the earth is an important factor in determining the length of our days and seasons. The earth's rotation and orbit around the sun at a constant tangential velocity create day and night, as well as the changing of seasons. It also has an impact on the weather patterns and ocean currents on earth.

4. Does the tangential velocity of the earth ever change?

Yes, the tangential velocity of the earth can change due to several factors, such as gravitational interactions with other planets and the moon, and changes in the earth's orbital path. However, these changes are relatively small and do not significantly affect our daily lives.

5. How is the tangential velocity of the earth related to the concept of centrifugal force?

The tangential velocity of the earth is a key factor in the concept of centrifugal force. As the earth orbits the sun, it experiences a centrifugal force that is equal and opposite to the gravitational force between the two bodies. This force helps to keep the earth in its orbit and maintain its tangential velocity.

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