How Do You Calculate Radial Acceleration at the Equator Due to Earth's Rotation?

In summary, the conversation revolves around finding the radial acceleration of a point on the surface of the Earth at the equator, due to the rotation of the Earth about its axis. The relevant equations for circular motion are discussed, including the relationship between centripetal acceleration and tangential velocity. The equation for angular velocity is also mentioned, as well as the need to convert units from kilometers to meters. Ultimately, the radial acceleration is calculated to be 0.0336 m/s^2.
  • #1
Amanda567
10
0
Knowing that the diameter of the Earth at the equator is 12 740 km, compute the radial acceleration of a point on the surface of the Earth at the equator, due to the rotation of the Earth about its axis.
 
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  • #2
Please make an attempt at this problem as part of your request. Hint: You are looking for the acceleration directed to the center of the rotation.

What equations do you think might be useful for circular motion?
 
  • #3
Sorry!
I know that centripetal acceleration is v^2/r
The diameter of the Earth is 12740 km, and half of that is the radius of 6370km.
How would I find v?
 
  • #4
You are getting closer. V is the tangential velocity, what is the equation for that?
 
  • #5
Would that be the period T, where that is the time to complete one revolution?
T=2pi(r)/v
 
  • #6
OK, Vt or tangential velocity = radius* angular velocity

What is the definition of angular velocity? You will need the 2*pi for sure, what else?
 
  • #7
Angular velocity is what represents speed?
by: F=d/dt (mv)
 
  • #8
Angular velocity or w= the change in the angle of rotation/ change in time

Think about our Earth making one complete rotation (how many radians is that?) divided by how long it takes to make that rotation in one day. Put that time in seconds.

Since you know the angular velocity multiply it by the radius to get Vt, the tangential velocity. Plug that value into V^2/r to get centripetal acceleration.

I get 3.33 E-2 m/s^2
 
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Likes muhammed_oli
  • #9
What is E-2?
 
  • #10
That means 3.33x10^-2 m/s^2 or 0.0333 m/s^2
 
  • #11
w=2pi/86400sec
w=0.00007
0.00007(6370km)=0.46324km/sec
vt=0.46324km^2/6370
vt=0.0000336

Thats what i get, what am i doing wrong?
 
  • #12
Change KM to meters which means you multiply your final result by 1000
 
  • #13
thanks so much!
 

1. What is the Radial Acceleration Problem?

The Radial Acceleration Problem is a phenomenon in physics where the observed acceleration of stars and galaxies in the outer regions of a galaxy is greater than could be explained by the visible matter within that galaxy. This led to the hypothesis of the existence of dark matter, which has yet to be directly observed.

2. How is the Radial Acceleration Problem measured?

The Radial Acceleration Problem is measured by observing the rotation curves of galaxies, which show the velocity of stars and gas at different distances from the center of the galaxy. By comparing these curves to the expected velocity based on the visible mass of the galaxy, scientists can determine the presence and amount of dark matter.

3. What are some proposed explanations for the Radial Acceleration Problem?

Some proposed explanations for the Radial Acceleration Problem include the existence of dark matter, modifications to the laws of gravity, and the possibility of a large number of small, dim stars that cannot be detected by current technology.

4. Is the Radial Acceleration Problem a well-established concept?

While the presence of dark matter and the Radial Acceleration Problem are widely accepted in the scientific community, there is ongoing debate and research on the exact nature of dark matter and its role in explaining the phenomenon. Therefore, it can be considered a well-established concept, but one that is still being actively studied.

5. How does the Radial Acceleration Problem relate to our understanding of the universe?

The Radial Acceleration Problem is an important puzzle in our understanding of the universe, as it challenges our current understanding of the laws of physics and the composition of the universe. By studying this phenomenon, scientists hope to gain a deeper understanding of the fundamental forces and components that make up our universe.

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