- #1
Irishwolf
- 9
- 0
Can somebody please explain ( properly)with examples , how the right hand rule describes the direction of coriolis acceleration? please!
Coriolis acceleration right hand rule? ?
- Thread starter Irishwolf
- Start date
In summary, the Coriolis force is something like v x omega and the cross product follows the right hand rule in a right handed coordinate system. To determine the direction of the Coriolis effect you take the cross product between your angular velocity and the velocity of the body.
- #2
Curl
- 758
- 0
the Coriolis force is something like v x omega and the cross product follows the right hand rule in a right handed coordinate system.
- #3
TheShrike
- 44
- 1
The Coriolis term is [itex]\textbf{}F_C{}[/itex] = -2m[itex]\textbf{}Ω[/itex][itex]\times[/itex][itex]\textbf{}v[/itex]
Where Ω is the angular velocity and v is the velocity of the body you are observing from the rotating reference frame.
To give an example imagine you are rotating with some constant angular velocity. For definiteness let's say you are rotating counter-clockwise. Then the angular velocity vector points upwards out of your head.
Now you observe a body somewhere around you. To determine the direction of the Coriolis effect you take the cross product between your angular velocity and the velocity of the body.
Again, for definiteness, let's say when you first observe the body it is directly in front of you and has a velocity to your left. (After this instant things will change of course, but that is what we are trying to find out).
Using the right-hand rule your thumb is pointing upwards in the direction of angular velocity. Your index finger points in the direction of the velocity of the body which should be to your left. Now your middle finger should point towards yourself, but there is a minus sign we must look at, so the Coriolis effect points outwards away from you, rather than towards you.
I hope that is correct and that it helps.
Where Ω is the angular velocity and v is the velocity of the body you are observing from the rotating reference frame.
To give an example imagine you are rotating with some constant angular velocity. For definiteness let's say you are rotating counter-clockwise. Then the angular velocity vector points upwards out of your head.
Now you observe a body somewhere around you. To determine the direction of the Coriolis effect you take the cross product between your angular velocity and the velocity of the body.
Again, for definiteness, let's say when you first observe the body it is directly in front of you and has a velocity to your left. (After this instant things will change of course, but that is what we are trying to find out).
Using the right-hand rule your thumb is pointing upwards in the direction of angular velocity. Your index finger points in the direction of the velocity of the body which should be to your left. Now your middle finger should point towards yourself, but there is a minus sign we must look at, so the Coriolis effect points outwards away from you, rather than towards you.
I hope that is correct and that it helps.
- #4
Irishwolf
- 9
- 0
Thanks that does help, but I am still puzzled on how to determine the cartesian coordinates (x,y,z) , for the rotating reference frame ? any ideas please?TheShrike said:The Coriolis term is [itex]\textbf{}F_C{}[/itex] = -2m[itex]\textbf{}Ω[/itex][itex]\times[/itex][itex]\textbf{}v[/itex]
Where Ω is the angular velocity and v is the velocity of the body you are observing from the rotating reference frame.
To give an example imagine you are rotating with some constant angular velocity. For definiteness let's say you are rotating counter-clockwise. Then the angular velocity vector points upwards out of your head.
Now you observe a body somewhere around you. To determine the direction of the Coriolis effect you take the cross product between your angular velocity and the velocity of the body.
Again, for definiteness, let's say when you first observe the body it is directly in front of you and has a velocity to your left. (After this instant things will change of course, but that is what we are trying to find out).
Using the right-hand rule your thumb is pointing upwards in the direction of angular velocity. Your index finger points in the direction of the velocity of the body which should be to your left. Now your middle finger should point towards yourself, but there is a minus sign we must look at, so the Coriolis effect points outwards away from you, rather than towards you.
I hope that is correct and that it helps.
- #5
PJC01
- 1,503
- 0
The right hand rule is a tool used to determine the direction of the Coriolis acceleration in a rotating reference frame. This rule states that if the right hand is placed with the thumb pointing in the direction of the rotation and the fingers pointing in the direction of the velocity, then the palm will point in the direction of the Coriolis acceleration.
To better understand this, let's look at an example. Imagine a person standing on the equator and throwing a ball towards the North Pole. In this scenario, the person is rotating with the Earth's rotation (velocity) and the ball is moving in a straight line towards the North Pole. According to the right hand rule, the palm of the hand will point towards the East, indicating that the Coriolis acceleration is acting in an eastward direction.
Another example is a hurricane in the Northern Hemisphere. As the hurricane moves towards the north, it experiences the rotation of the Earth, causing the Coriolis acceleration to act towards the east. This is why hurricanes in the Northern Hemisphere rotate in a counterclockwise direction.
In summary, the right hand rule helps us understand the direction of the Coriolis acceleration in a rotating reference frame. By using this rule, we can determine the direction of the acceleration and better understand its effects on various phenomena, such as the rotation of hurricanes and the movement of objects on a rotating surface.
FAQ: Coriolis acceleration right hand rule? ?
1. What is Coriolis acceleration?
Coriolis acceleration is a phenomenon that occurs due to the rotation of the Earth. It is an apparent acceleration experienced by objects moving on a rotating body, such as the Earth, and is responsible for the deflection of objects moving in a straight line relative to the rotating body.
2. How is Coriolis acceleration calculated?
The Coriolis acceleration is calculated using the formula a = 2Ω x v, where a is the Coriolis acceleration, Ω is the angular velocity of the rotating body, and v is the velocity of the moving object. This formula follows the right hand rule, where the direction of the acceleration is perpendicular to both the angular velocity and the velocity of the object.
3. What is the purpose of the right hand rule in Coriolis acceleration?
The right hand rule is used to determine the direction of the Coriolis acceleration. By pointing the thumb of the right hand in the direction of the angular velocity and the fingers in the direction of the velocity of the object, the direction of the acceleration can be determined by the direction in which the palm is facing.
4. Is the Coriolis acceleration the same at all latitudes?
No, the Coriolis acceleration varies with latitude. As the Earth is a rotating sphere, the angular velocity changes with latitude, resulting in a varying Coriolis acceleration. This is why the Coriolis effect is stronger near the poles and weaker near the equator.
5. How does the Coriolis acceleration affect weather patterns?
The Coriolis acceleration plays a significant role in the formation of weather patterns. It causes air and water masses in the atmosphere and oceans to deflect, which creates circulation patterns such as hurricanes and typhoons. These patterns are important for regulating the Earth's climate and weather systems.