# Coriolis forces, rotating coordinate systems

• bcoats
In summary, the conversation discusses the confusion and frustration experienced by the speaker while studying Symon's Mechanics 3rd Ed. Specifically, they mention the difficulty in understanding Chapter 7 on rotating coordinate systems, as it lacks examples and uses complex notation. The conversation also mentions a specific problem in the chapter, 7.7, and the struggle to solve it without clear guidance. The speaker expresses their wish for a website or companion book that provides step-by-step examples for solving these types of problems. Overall, the conversation highlights the challenges of studying Symon's Mechanics and the speaker's regret in choosing to major in Physics.
bcoats
I know that some people worship Symon's Mechanics 3rd Ed., but I find this book incredibly confusing...especially chapter 7, dealing with rotating coordinate systems. I follow the math, and perhaps the logic, but I can't even find a way to start the homework problems. The guy doesn't give any examples, and how the hell is one supposed to learn how to solve a problem when provided with nothing but dense proofs using strange notation?

For example, problem 7.7 tells us that a body is dropped from height h above the earth. We are to calculate the coriolis force as a function of time, given that it has a negligible effect on the motion, and using the velocity of a freely falling body with acceleration Ge. Neglect air resistance, assume h is small so that Ge can be taken as constant. Then, calculate the net displacement ofthe point of impact due to the coriolis force calculated previously.

OK , so Symon proves that Ge(r)=g(r)-w x (w x r). (The w represents omega, the Ge represents vector g subscript e.) I guess the coriolis force is the -2mw x d*r/dt term. How are we supposed to solve this. Are we just supposed to KNOW what w is? Nowhere in this chapter is w given for earth. I would think that maybe it would be (2pi/24hrs)*theta^ (if theta^=theta hat=unit vector in theta direction). Unfortunately, like Symon my professor rarely works examples either. I have no clue how to go about solving this or most other problems in the book. I there a website out there that, say, gives clear, step-by-step examples for solving these type of problems? Or does anyone write a "companion book" to be read side-by-side with Symon's that actually works examples for problems like his?

Why the heck did I major in Physics?
Ben

The only person I ever heard mention Symon on this forum is me! But I do it for 5 I think because it's the only mechanics book I've read. :P

I wrote a light "summary" of the chapter on rotating coordinate systems a while back that at least answers your uncertainty regarding that the coriolis force is. Here's the thread.

You should read the chapter until you understand every single little detail about it as if you'd yourself written it. Then no problem should pose conceptual difficulties. (In theory )

## 1. What are Coriolis forces?

Coriolis forces are a type of inertial force that arises due to the rotation of the Earth. They are experienced as a deflection of moving objects on the Earth's surface, such as winds and ocean currents, and are caused by the Earth's rotation on its axis.

## 2. How do Coriolis forces affect weather patterns?

Coriolis forces play a significant role in shaping global weather patterns. They cause winds to rotate clockwise in the Southern Hemisphere and counterclockwise in the Northern Hemisphere, leading to the formation of high and low-pressure systems and the development of storms and hurricanes.

## 3. Do Coriolis forces impact the trajectory of objects in space?

Yes, Coriolis forces also affect the trajectory of objects in space. This is particularly important for long-range missiles and satellites, as the rotation of the Earth can cause them to deviate from their intended paths. As a result, scientists must account for Coriolis forces when calculating the trajectory of objects in space.

## 4. What is a rotating coordinate system?

A rotating coordinate system is a mathematical framework used to describe the motion of objects in a rotating reference frame. It takes into account the Earth's rotation and allows scientists to accurately analyze and predict the behavior of objects moving on or near the Earth's surface.

## 5. How do Coriolis forces impact ocean currents?

Similar to their effect on winds, Coriolis forces also affect ocean currents. In the Northern Hemisphere, ocean currents are deflected to the right due to Coriolis forces, while in the Southern Hemisphere, they are deflected to the left. This can lead to the formation of gyres and the redistribution of heat and nutrients in the ocean.

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