Centripetal Forces The Coriolis Force The Geostrophic Wind
In lecture, we touched briefly upon the concept that a force is the product of a mass times an acceleration. An object that is under the influence of a net force will experience an acceleration. An acceleration is a change in velocity with res pect to time.
We will learn today that objects that are moving in curved or circular paths are subjected to forces called centripetal forces.
Centripetal Forces
Objects moving in a circular path are subjected to accelerations. Consider what happens when you travel around a bend in the road. You are shifted around due to forces incurred upon you as you travel in a circular path.
These forces that occur with circular motion can be seen in many places in the everyday world. A rollercoaster going up and around a loop is one such example. The planets maintain constant orbits around the sun due to these forces accompanied by circ ular motion.
The magnitude of a centripetal force is defined by the mass of an object and its centripetal acceleration. Remember that a force is the product of a mass and an acceleration, and a centripetal force is the product of a mass and its centripetal acceler ation. Centripetal acceleration is defined as an object's tangential velocity squared divided by its radius of curvature.
The Coriolis Force
The Coriolis Force is the force imparted on objects that are in motion on the Earth's surface. The force is due to the circular motion of the Earth's rotation. We said that objects moving in a circular path are subjected to forces. Objects in motion on the Earth's surface are moving relative to their frame of reference, but are also moving with the Earth as it rotates. They are being subjected to a Coriolis Force.
Since a force will cause a mass to accelerate, Coriolis Forces greatly effect the gases of the Earth's atmosphere as they move about from one location to another.
It turns out that the magnitude of the Coriolis Force that is exerted on an Earth based object in motion is proportional to its velocity as well as its position on the Earth's surface.
The formula for the magnitude of the Coriolis Force is 2 * Earth's angular velocity * sin latitude * velocity. Angular velocity refers to the number of degrees an object rotates in a given amount of time. It is typically represented in the form of ra dians per second. Remember that there are 2*pi radians in 360 degrees. The Earth's angular velocity is 7.29 * 10^-5 radians/second. What would be the Earth's angular velocity in units of degrees/day?
The Coriolis Force acts to the right of the direction of motion of the wind in the northern hemisphere and to the left of the direction of motion in the southern hemisphere.
Notice that the Coriolis Force depends not only on how fast an object is moving, but also its latitude on the Earth. The Coriolis Force is a function of the sine of the latitude where 0 degrees is the Equator and 90 degrees would be the poles. Since the sine of 0 is 0, the magnitude of the Coriolis Force is 0 at the Equator and since the sine of 90 degrees is 1, the magnitude of the Coriolis Force is a maximum at the poles.
Implications of the Coriolis Force on the winds
We have learned that the Coriolis Force will accelerate a wind to the right of its direction of movement in the Northern Hemisphere and the further north in latitude, the stronger the magnitude of the Coriolis Force.
Let's now extend our discussion to the consideration of high pressure systems and low pressure systems. We know that winds will blow from regions of higher pressure toward regions of lower pressure. In lecture we will learn why winds blow clockwise ar ound high pressure and counterclockwise around low pressure.
The Geostrophic Wind
Consider wind moving in a non-rotating reference frame. Wind will be generated by the pressure gradient force which is a change in pressure across a horizontal distance. However, when we factor in the Coriolis Force, which is the force generated by t he Earth's rotation, we observe the wind will be deflected to the right (in the northern hemisphere) of its direction of motion.
The geostrophic assumption states that the magnitude of the Coriolis Force will be approximately equal to the pressure gradient force in the midlatitudes (between 30 and 60 degrees). It turns out that the wind will be deflected at such a way su ch that it will blow somewhat parallel to the isobars.