Acceleration in a rotating frame

In summary, the conversation is about a derivation involving Newton's second law in a rotating frame. The final line is causing confusion about the signs of the Coriolis and centrifugal forces and the net force measured in the rotating frame. The person named Daniel clarifies that the net force should only include external forces and not inertial forces. However, there is still confusion about the signs of the forces in the final equation.
  • #1
Nylex
552
2
I'm getting confused by this. I have a handout from a lecture that has a derivation that ends with

"[tex]\vec{a} = \vec{a'} + 2\vec{\omega} \times \vec{v'} + \vec{\omega} \times (\vec{\omega} \times \vec{r})[/tex]

Multiplying through by mass, m

[tex]m\vec{a} = \vec{F_{ext}} = m\vec{a'} + 2m\vec{\omega} \times \vec{v'} + m\vec{\omega} \times (\vec{\omega} \times \vec{r})[/tex]

We preserve Newton II in rotating frame by writing [tex]\vec{F'_{net}} = m\vec{a'}[/tex] where [tex]\vec{F'_{net}}[/tex] is the net force measured by observer in rotating frame.

ie. [tex]\vec{F'_{net}} = \vec{F_{ext}} - 2m(\vec{\omega} \times \vec{v'}) - m[\vec{\omega} \times (\vec{\omega} \times \vec{r})][/tex]"

It's really the last line that's confusing me. The expressions for the Coriolis and centrifugal forces are

[tex]\vec{F_{Cor}} = -2m(\vec{\omega} \times \vec{v'})[/tex] and [tex]\vec{F_{cent}} = -m\vec{\omega} \times (\vec{\omega} \times \vec{r})[/tex], so why isn't it

[tex]\vec{F'_{net}} - \vec{F_{Cor}} - \vec{F_{cent}} = \vec{F_{ext}}[/tex]?
 
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  • #2
Hold on a second,who's [itex] \vec{F}_{ext} [/itex]...?

Daniel.
 
  • #3
"Sum of real forces (electrical, magnetic, gravitational, etc); only these forces are observed in stationary frame".

All I'm getting confused about is the signs of those forces.
 
  • #4
Why shouldn't the NET force be the sum of all external forces...?Afer all,both Coriolis & centrifugal are inertial forces,they're not external forces.

Daniel.
 
  • #5
Grr, I know that, but:

[tex]m\vec{a} = \vec{F_{ext}} = m\vec{a'} + 2m\vec{\omega} \times \vec{v'} + m\vec{\omega} \times (\vec{\omega} \times \vec{r})[/tex]

ie. [tex]\vec{F'_{net}} = \vec{F_{ext}} - 2m(\vec{\omega} \times \vec{v'}) - m[\vec{\omega} \times (\vec{\omega} \times \vec{r})][/tex]"

The first and second lines aren't the same. If [tex]\vec{F'_{net}} = m\vec{a'}[/tex], then the first line is [tex]m\vec{a} = \vec{F_{ext}} = \vec{F'_{net}} - \vec{F_{Cor}} - \vec{F_{cent}}[/tex] :confused:.
 
Last edited:

Related to Acceleration in a rotating frame

1. What is acceleration in a rotating frame?

Acceleration in a rotating frame refers to the change in velocity of an object as it moves in a rotating coordinate system. This type of acceleration can be caused by the rotation of the coordinate system itself, or by the object moving in a circular path within the rotating frame.

2. How is acceleration in a rotating frame different from linear acceleration?

Acceleration in a rotating frame is different from linear acceleration in that it takes into account the effects of the rotating coordinate system. In a linear acceleration, the velocity of an object changes in a straight line, whereas in a rotating frame, the velocity changes along a curved path due to the rotation of the coordinate system.

3. What is the Coriolis effect and how does it relate to acceleration in a rotating frame?

The Coriolis effect is a phenomenon where an object moving in a rotating frame experiences a force that is perpendicular to its direction of motion. This force is caused by the change in velocity due to the rotation of the coordinate system, and it is a key component of acceleration in a rotating frame.

4. How is acceleration in a rotating frame used in real-world applications?

Acceleration in a rotating frame is used in various real-world applications, such as in navigation systems, aerospace engineering, and weather forecasting. It helps to accurately determine the motion and forces acting on objects in a rotating frame, which is essential for safe and efficient operation of many systems.

5. What are some common misconceptions about acceleration in a rotating frame?

One common misconception about acceleration in a rotating frame is that it is the same as centrifugal force. While both concepts are related to rotational motion, acceleration in a rotating frame is a measurable physical quantity, whereas centrifugal force is a fictitious force that only appears to act on objects in a rotating frame.

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