Coriolis Acceleration: Anti-Clockwise vs Radial Velocity

[Lee333]

http://imgur.com/euMW6FO
In the above question, why is coriolis acceleration in the positive eθ direction?. The system is rotating in an anti-clockwise direction, and in the er direction the velocity of the cam is
radially outwards. Would this mean that the coriolis acceleration is to the right of this velocity and thus in the negitive eθ direction?

 

[voko]

The Coriolis acceleration is defined from the point of view in the co-rotating frame, and it would be $-2 \dot{r} \dot{\theta}$, against the rotation.

 

[A.T.]

If unsure about the direction use the cross product definition:

https://en.wikipedia.org/wiki/Coriolis_effect#Formula

Then use the right-hand-rule. Or the left-hand-rule to account for the minus sign in the definition, or the right-hand-rule but swap the cross product operands.

Which makes me wonder: Why do they write the definition in that order and add the minus sign? This seems to be a convention for all inertial forces in the rotating frame:

https://en.wikipedia.org/wiki/Rotating_reference_frame#Newton.27s_second_law_in_the_two_frames

Why not swap the operands, and drop the minus sign? Is it make it them look like the linear inertial force -ma?

 

[voko]

In the non-inertial frame, a distinction is made between the "apparent" acceleration, which is treated as the acceleration in Newton's second law for the rotating frame, and three other terms, which are considered the effect of inertial forces and are tossed over to the other side of Newton's second law.

 

[pmacias]

Coriolis acceleration is a result of the Coriolis effect, which is the apparent deflection of objects or fluids moving in a rotating system. In this case, the system is rotating in an anti-clockwise direction, meaning that the angular velocity is also in the anti-clockwise direction. This creates a Coriolis acceleration that is in the positive eθ direction, which is perpendicular to both the angular velocity and the radial velocity.

The direction of the Coriolis acceleration is determined by the right-hand rule, where the direction of the acceleration is perpendicular to both the velocity and the rotation. In this case, the radial velocity is pointing outwards, while the angular velocity is pointing in the anti-clockwise direction. Using the right-hand rule, we can see that the Coriolis acceleration will be in the positive eθ direction, which is to the right of the radial velocity.

Therefore, the Coriolis acceleration in this system will be in the positive eθ direction, not the negative eθ direction as suggested in the question. It is important to note that the direction of the Coriolis acceleration is dependent on the direction of rotation and the velocity of the object, and may vary in different systems.