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## Rocket from the North Pole: Instructor's Guide

### Main Ideas

Provides an intuitive understanding of Coriolis acceleration.

Estimated Time: 10 minutes, including wrap-up

The inflated balloon represents the surface of the Earth (which is rotating at constant angular velocity). Shoot a rocket from the North Pole that is initially aiming to fly over the heads of point X on the equator. Assume there is no air resistance, and no left/right boosters on the rocket, Draw the trajectory onto the balloon as the rocket flies from the north pole to the equator.

• In the earth's frame, the trajectory can be described by a Coriolis force pointing eastward or westward? (Alternately, what is the direction of the Coriolis acceleration relative to the direction of motion?
• Continue drawing the trajectory southward. Does the Coriolis force reverse direction?
• Will the rocket fly over the South Pole?
• Is there a Coriolis force as the rocket passes the equator?

### Prerequisite Knowledge

• some familiarity with Coriolis acceleration

### Props/Equipment

• balloons (or other large spherical objects which can be written on)
• markers

### Student Conversations

• Students have trouble (a) spinning the balloon or globe with a constant angular speed and (b) if using the globes, the pen gets caught on the seams.
• Some students notice that the curvature of the trajectory drawn on the balloon is larger (tighter curl) near the pole than near the equator (this is because the velocity relative to the earth is smaller near the poles - the pen crosses each lines of latitude in equal time intervals, but the tangential speed of the surface of the earth is larger near the equator - in the earth frame, one can describes this as a result of the centrifugal acceleration).
• Students tend to focus only on the Coriolis acceleration, but the trajectory is influence by the centrifugal acceleration as well.
• Some students need help in understanding that, although the Coriolis acceleration changes direction at the equator, the Coriolis acceleration is not zero at the equator, but is perpendicular to the surface of the earth.
• Continue to emphasize that the Coriolis acceleration is perpendicular to the velocity relative to the surface, so it does not cause a change in speed relative to the surface (only a change in direction). The centrifugal acceleration is radially outward and everywhere other than the equator (and the poles), there is a non-zero projection on the surface of the earth towards the equator, and causes a change in speed relative to the surface of the earth.
• Coriolis acceleration is to the right of the direction of motion in the northern hemisphere and to the left in the southern hemisphere
• The component of the Coriolis force tangent to the surface switches direction
• The rocket will go over the south pole - these two points match in the two reference frames so if it happens in one, it happens in the other
• Yes - there is a Coriolis force at the equator!! it's just perpendicular to the surface toward the center of the earth.

### Wrap-Up

Discuss the questions above.

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