- #1
Habeebe
- 38
- 1
Homework Statement
A puck slides with speed v on a frictionless ice that is level in the sense that the surface is perpendicular to geff at all points. Show that the puck moves in a circle as viewed in the Earth's rotating frame. Determine the radius of the circle and the angular frequency of the motion. Assume that the puck's circle is small compared to the radius of the earth.
Homework Equations
[itex]\vec{F}_{cor}=2m\vec{v}\times\Omega[/itex]
The Attempt at a Solution
I have a solution, I just want to make sure that my logic is correct. I'm worried that I'm missing something subtle.
Assuming that geff the normal force and the z component of the Coriolis force all balance (it's sitting on top of the ice at all times). Then the only thing I have to worry about is the Coriolis force.
[itex]\vec{F}_{cor}=2m\vec{v}\times\Omega[/itex] dot product by v on both sides
[itex]\vec{F}_{cor}\cdot\vec{v} = 2m(\vec{v}\times\Omega)\cdot\vec{v} [/itex]
[itex](\vec{v}\times\Omega)\cdot\vec{v} = 0 [/itex] therefore:
[itex]\vec{F}_{cor}\cdot\vec{v}=0[/itex] therefore, [itex]\vec{F}_{cor}\perp\vec{v}, \forall\vec{v}[/itex]
Since the force is perpendicular to the velocity, it must go in a circle.