Background

The "coriolis effect" dramatically influences the circulation of both the atmosphere and oceans. In the atmosphere, the coriolis effect causes circulation to break into 3 circulation cells in each hemisphere (northern and southern), called "Hadley Cells". Without the coriolis effect, winds would tend to blow from north to south, making the cold climate extend further south. The coriolis effect also causes ocean currents to be more intense in the western ocean basins. The Gulf Stream is an example of this. Another important consequence is that large storms and tornadoes circulate counter-clockwise in the northern hemisphere. The strength of the coriolis effect varies with latitude. It is weakest near the equator and strongest at the poles.

On the rotating earth, moving bodies appear to curve to the right in the northern hemisphere and curve to the left in the southern hemisphere. This exercise demonstrates how this could be true.

The first page of this exercise is named "Fixed Reference Frame: The Stars". The second page follows this one and is named: "Rotating Reference Frame: The Earth"  If the copying of these pages went well, when the pages are placed on top of each other and lined up, the exact centers of the globe ("X" on "Fixed Reference Frame") should overlay the center of the earth on the "Rotating Reference Frame" sheet. 

The view is straight down on the North Pole. The earth rotates counter-clockwise from this view. Can you visualize why this is so, based on the sun rising in the east and setting in the west? The "Fixed Reference Frame" page and the "Rotating Reference Frame" pages should be removed from the book and laid on top of each other, with each page face up. The "Fixed Reference Frame" page should be on top.

Our viewpoint is that of the "Fixed Reference Frame"  It is also called an "inertial frame" because a body in motion, with no forces (like gravity) acting on it, will travel in a straight line at a constant velocity. So, from our point of view in outer space, the stars don't move (at least very much) and objects travel in straight lines.

Notice on the top sheet, two paths (path A and path B) are indicated. Path A represents an object launched outward from the North Pole. For path B, the object is launched nearer to the equator, in a direction toward the North Pole. But, in the inertial reference frame, there is also a tangential velocity due to the earth's rotation. Even though we don't notice it very much, at the equator the earth's surface has a speed of 1,667 km/hr, or about 1,000 miles per hr, which is faster than the speed of sound (how can this be?). But, path A begins at the North Pole, which does not move due to the earth's rotation, so we don't need to put in a tangential velocity component.

On the bottom sheet, the straight-line paths are copied from the top sheet, just for reference. Do you think the moving body will travel along these paths?

The two paths have small circles drawn on them that are points where we will mark the progress of the body along its straight-line path. The marks are on a straight line, but on the rotating earth below, that will not be the case!

Steps:

1. First, print pages 2 and 3..

2. Cut out the little box on the top sheet of the "Fixed Reference Frame". Use whatever tool you have handy. Neatness is not really necessary.

2. Notice that there are 2 dotted lines on the top sheet, labeled Path A and Path B. These are the paths of the moving body in the inertial, or fixed reference frame. Notice that they are straight lines, because in an inertial reference frame bodies move in straight lines.  Each path has small circles marked on it. On the top sheet only, pierce with a pin or ballpoint pen at the center of each circle, so that you can make a mark on the sheet below when the bottom sheet is placed beneath.

3. Next, place top sheet exactly lined up with bottom sheet so that the centers of the globes on each sheet are aligned. Stick a tack, pin, or pen point thru the "X" point at the center of the circle on the top sheet. After you do this, check to see that you have also pierced the center of the globe on the bottom sheet.  The "0" from the bottom sheet should be centered in the cutout box of the top sheet.

Next, you will use the top sheet as a template for marks on the bottom sheet, which will be rotated underneath the top sheet, just like the real earth rotates.

4. Mark the start point of path B. The start point of path A is the center, so it does not need marking.

5. Now, rotate the bottom sheet (center point of globes still pinned so the sheets rotate about that center) until the "1" shows in the cutout box. Mark the bottom sheet at position "1" on each of Path A and Path B (of the top sheet).

6. Rotate the bottom sheet so that the number "2" is showing in the cutout box, and mark the bottom sheet at point 2 on paths A and B.

7. Continue the procedure with points 3 and 4.

8. Separate the two sheets and locate the marks you made in steps 4 to 7. Draw a smooth, continuous curve between the marks. The points should follow a curved path.  This is the path that an observer on the rotating earth would see.

Complications:

This exercise correctly shows the important features of the coriolis effect. However, the astute student might ask: how can the body be moving in an inertial frame if it is being acted upon by the force of the earth's gravity? Good question! The earth's gravitational field does not act on the body (atmosphere, currents, rockets, etc) in its direction along its path, though, so we don't have to take it into account. However, the important component of the body's velocity is the velocity toward the North Pole, from the viewpoint of the outside observer. At the equator, the body is moving straight toward the observer, and the coriolis force is zero. As the body moves farther away from the equator, the observer sees it moving closer to the pole, and the coriolis effect strengthens.

1. The coriolis effect is strongest at the poles and weakest at the equator
2. The motion of a massive body (projectile, water in an ocean current, air flowing) veers to the right in the northern hemisphere and to the left in the sourthern hemisphere.