# Tangential Component of Centrifugal Acceleration

• SebastianRM
In summary, the conversation discusses the calculation of the tangential component of the centrifugal force, which is related to the angle between the centrifugal force and the axis normal to the direction of the gravitational force. The angle is determined by geometry and is equal to θ, the complement of the angle of latitude. The magnitude of the centrifugal acceleration is determined by the equation acf = Ω^2Rsinθ. A diagram is provided to clarify the concept and it is shown that the angle in question is equal to θ. The conversation ends with a thank you from the original poster for the clarification.
SebastianRM
The thing is in page p.347 Taylor, it is said that the component is:

g_tan = Omega^2*Rsin(theta)cos(theta) However the angle between the centrifugal Force and the axis normal to the direction of the grav Force is actually 90 - theta, I am not really getting where I am going wrong understanding this.

The angle in question is between the perpendicular to the Earth's axis (the direction of the centrifugal force component) and a tangent to the surface. That angle is θ which you can see by geometry. θ is the complement of the angle of latitude, L (θ = 90-L).

The magnitude of the centrifugal acceleration (see equation 9.43) is: acf = Ω2Rsinθ. So the tangential component is acfcosθ. At the equator, where θ is 90° (L=0), the centrifugal force is maximum (sinθ = 1) but the tangential component is 0 because it is all in the radial direction (cosθ = 0). Towards the pole, the direction is almost tangential (cosθ=1) but the magnitude of the centrifugal force approaches 0 (sinθ = 0).

AM

SebastianRM
kuruman said:
I thought I explained that to you here.
If there is something you still did not understand, you should have responded there instead of starting a new thread. In any case, post a drawing of what you think is the case. I suspect you have misidentified something.
Sorry about that, I could not track the post I had done already. Here is the sketch of how I am working it out on my mind.
https://imgur.com/spbCzfS
Since he says: 'the tangential component of g (the component normal to the true grav force)'

SebastianRM said:
Sorry about that, I could not track the post I had done already. Here is the sketch of how I am working it out on my mind.
https://imgur.com/spbCzfS
Since he says: 'the tangential component of g (the component normal to the true grav force)'
In the drawing you have provided, you have shown two angles of 90-θ making up a right angle! The angle between the Fcf vector and the tangent is 90 - (90-θ) = θ! (the angle of the tangent to the radial vector being necessarily a right angle).

AM

SebastianRM
To supplement post #5 by @Andrew Mason, it is known from geometry that two angles that have their sides mutually perpendicular are equal. In your diagram, the z-axis (along Ω) is perpendicular to Fcf and the radial vector is perpendicular to the tangential component (not shown). Therefore the angle that you show as θ is equal to the angle formed by Fcf and the tangential direction.

SebastianRM
Thank you so much guys! I see it now!

kuruman

## 1. What is the Tangential Component of Centrifugal Acceleration?

The Tangential Component of Centrifugal Acceleration is the component of the acceleration experienced by an object moving in a circular path that is perpendicular to the radius of the circle. It is also known as the radial acceleration and is responsible for the change in direction of the object's velocity.

## 2. How is the Tangential Component of Centrifugal Acceleration calculated?

The Tangential Component of Centrifugal Acceleration can be calculated using the formula: at = ω²r, where at is the tangential acceleration, ω is the angular velocity, and r is the radius of the circular path.

## 3. What is the difference between Tangential Component of Centrifugal Acceleration and Centripetal Acceleration?

The Tangential Component of Centrifugal Acceleration and Centripetal Acceleration are two components of the total acceleration experienced by an object moving in a circular path. The tangential component is responsible for the change in direction of the object's velocity, while the centripetal component is responsible for the change in magnitude of the object's velocity.

## 4. What are some real-world examples of Tangential Component of Centrifugal Acceleration?

Some real-world examples of Tangential Component of Centrifugal Acceleration include the acceleration experienced by a car moving around a curved road, the acceleration experienced by a satellite orbiting around the Earth, and the acceleration experienced by a rollercoaster moving around a loop.

## 5. How does the Tangential Component of Centrifugal Acceleration affect the stability of an object in circular motion?

The Tangential Component of Centrifugal Acceleration affects the stability of an object in circular motion by causing it to continually change direction. If the centripetal force is not strong enough to counteract the tangential component, the object may lose stability and fly off its circular path.

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