Puck in Ice, coriolis force

[m0nk3y]

Show that the Coriolis force makes the puck move in a circle as seen in Earth's rotating frame


I need help setting this up!

Homework Equations

-2m$$\varpi$$x v

The Attempt at a Solution

So far i have a drawing
The Earth on an xyz axis, z up, y across, and x in an out of paper.
the puck is on the surface the earth, it coordinate system is, directly abouve the puck pointing towards the north pull we have the y axis, its z axis extends from the origin of the Earth and its x-axis is going into and out of the paper.

I need help setting up the $$\varpi$$

THANK you in advance, i know this will be hard to understand.

 

[Jhero]

Hello!

To show that the Coriolis force makes the puck move in a circle, we first need to understand the Coriolis force. The Coriolis force is a fictitious force that appears to act on objects moving in a rotating reference frame. In this case, the reference frame is Earth's rotating frame, with the origin at the center of the Earth and the z-axis pointing towards the North Pole.

To set up the equation for the Coriolis force, we need to first define some variables. Let's say that the puck has a mass of m and is moving with a velocity v in the x-direction. The Coriolis force, Fc, can be calculated using the formula Fc = -2mω×v, where ω is the angular velocity of the rotating frame.

Next, we need to determine the direction of the Coriolis force. Since the puck is moving in the x-direction, the Coriolis force will act in the y-direction, perpendicular to the puck's velocity. This can be represented as Fc = -2mωvz, where vz is the component of the puck's velocity in the z-direction.

Now, let's consider the motion of the puck in the rotating frame. Since the puck is moving in a straight line in the x-direction, it will appear to be moving in a circular path in the rotating frame due to the Coriolis force acting on it. This is because the Coriolis force acts perpendicular to the puck's velocity, causing it to change direction and move in a circular path.

To better understand this, let's break down the Coriolis force equation. The -2m term represents the strength of the force, while ω represents the angular velocity of the rotating frame, which is determined by the Earth's rotation. The v term represents the puck's velocity, and the vz term represents the component of the puck's velocity in the z-direction.

In conclusion, the Coriolis force, when acting on a moving object in Earth's rotating frame, causes the object to move in a circular path. This is due to the perpendicular nature of the force to the object's velocity, causing it to change direction and move in a circular path. I hope this helps to set up the equation for the Coriolis force and understand its role in making the puck move in a circle in Earth's rotating frame.