Does rotational motion affect the translational motion?

• Avijit
In summary, in a scenario where a flying object is moving in 3D space and rotating, a Coriolis force (ω×ν) will exist in the body attached frame due to the effects of translation and rotation. However, in the inertial frame, there will be no equivalent force of ω×ν as inertial forces only exist in non-inertial frames.
Avijit
A flying object is moving in 3D space having translational velocity and the object is also rotating. Consider a body frame (xb-yb-zb) attached to the C.G of the moving body. Hence the body attached frame is also translating and rotating (as the object is flying) with respect to a fixed inertial frame. The inertial frame(X-Y-Z) is attached and fixed at some specific location on ground(earth). Due to the effect of both translation and rotation a Coriolis kind of force (rotational velocity cross translational velocity) ω×ν will exist in body attached frame (xb-yb-zb). Here ω: Rotational velocity of the flying object, v: velocity of the object represented in body attached frame (xb-yb-zb).

I would like to know :
Does any equivalent force of ω×ν will exist in the inertial frame? In other words, using the frame transformation (from body attached frame to inertial frame) can we realize the ω×ν effect in inertial frame?

In your described scenario, every point in the body is at rest with respect to the rotating coordinates, so there's no Coriolis force. Remember the rotating reference frame is attached to the center of mass of the object, so there's no translational velocity in that frame.

here is the equation in body fixed frame
where U V W are velocity component of moving body represented in body frame. P Q R are body rotation rates in respective direction

Last edited:
Avijit said:
Does any equivalent force of ω×ν will exist in the inertial frame?
No, inertial forces exist only in non-inertial frames.

What is rotational motion?

Rotational motion is the movement of an object around a fixed point or axis. This can involve spinning, rolling, or twisting.

What is translational motion?

Translational motion is the movement of an object in a straight line, without any rotation.

How are rotational and translational motion related?

Rotational motion can affect translational motion, as the two are interconnected. The direction and speed of an object's rotational motion can impact its overall translational motion.

Can rotational motion cause translational motion?

Yes, rotational motion can cause translational motion. For example, when a wheel rotates, it also moves forward in a straight line, demonstrating the relationship between the two types of motion.

Does rotational motion always affect translational motion?

No, rotational motion does not always affect translational motion. In some cases, an object may have rotational motion but not experience any net translational motion, such as a spinning top on a flat surface.

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