Use angular momentum arguments to describe why a parcel of air moving from the equator towards the North Pole will be deflected to the east. It may be helpful to show equations in your response.
To understand why a parcel of air moving from the equator towards the North Pole is deflected to the east, we can use the concept of angular momentum and the Coriolis effect. Angular momentum is a property of rotating systems and is described by the equation:
L = mvRsin(θ)
Where L represents angular momentum, m is the mass of the object, v is its velocity, R is the distance from the axis of rotation, and θ is the angle between the velocity vector and the radial direction.
In the case of air moving from the equator towards the North Pole, the velocity vector points towards the pole. As the parcel moves closer to the pole, its distance from the axis of rotation decreases (R becomes smaller). Since the mass of air remains constant, any change in R will cause a change in angular momentum (L).
According to the conservation of angular momentum, if the distance from the axis of rotation decreases (R becomes smaller), the velocity (v) must increase to maintain a constant angular momentum. Therefore, the parcel of air will start speeding up as it moves towards the pole.
Now, let's consider the Coriolis effect. The Coriolis effect is an apparent deflection of the path of an object moving in a rotating system, like the Earth. It is caused due to the rotation of the Earth underneath the object.
In the Northern Hemisphere, the Coriolis effect causes the moving air to be deflected to the right (East) relative to its trajectory. The deflection is the strongest at the poles and gradually decreases towards the equator.
As the parcel of air moves towards the pole, its speed increases due to the conservation of angular momentum. Simultaneously, the Coriolis effect deflects it towards the right (East). So, as a result of both factors, the air mass is deflected to the east as it moves towards the North Pole.
It's important to note that the deflection direction would be to the left (West) for air moving from the equator towards the South Pole, based on the same reasoning described above.
Overall, the combination of the conservation of angular momentum and the Coriolis effect results in the deflection of air masses towards the east as they move from the equator towards the North Pole.