# Calculating Yaw Rate & Angle of Rotating Body w/ Offset C.o.M.

• tuoni
The term "wobble" can be used to describe the movement of the body as it rotates, but it is not a commonly used term in this context.
tuoni
Is it possible to calculate the yaw rate (rad/s) or yaw angle (rad) of a rotating body where centre of mass does not coincide with the rotational axis?

E.g. a tyre rim of radius r, spinning at angular velocity ω, and with its centre of mass rx off-centre relative to the rotational axis. The faster you spin it, the faster it would "wobble."

Can this be calculated?

EDIT:

I've tried searching for this but so far I have found nothing...maybe this isn't the terminology commonly used?

Last edited:
Yes, it is possible to calculate the yaw rate or yaw angle of a rotating body where the center of mass does not coincide with the rotational axis. The equations for calculating the yaw rate are as follows: Yaw rate (rad/s): ωyaw = (rx/r)ωYaw angle (rad): θyaw = (rx/r)θWhere ω is the angular velocity, rx is the distance between the center of mass and the rotational axis, r is the radius of the body, and θ is the angular displacement.

## 1. How is yaw rate calculated?

The yaw rate of a rotating body is calculated by dividing the change in its angular displacement by the change in time. This can be represented by the formula: yaw rate = Δθ/Δt, where Δθ is the change in angular displacement and Δt is the change in time.

## 2. What is the formula for calculating angle of rotation?

The angle of rotation, also known as the yaw angle, can be calculated using the formula: θ = ωt + θ0, where ω is the angular velocity, t is the time, and θ0 is the initial angle of rotation.

## 3. How does the offset of the center of mass affect the calculation of yaw rate and angle of rotation?

The offset of the center of mass affects the calculation of yaw rate and angle of rotation by introducing an additional moment of inertia. This means that the body's mass is distributed unevenly, causing it to rotate differently than a body with a symmetrical mass distribution.

## 4. Can yaw rate and angle of rotation be calculated for any rotating body?

Yes, yaw rate and angle of rotation can be calculated for any rotating body, as long as its angular displacement and time are known. However, the accuracy of the calculation may be affected by factors such as the body's shape, mass distribution, and external forces.

## 5. How are yaw rate and angle of rotation used in real-world applications?

Yaw rate and angle of rotation are important parameters in various fields such as engineering, physics, and navigation. They are used to analyze the motion of rotating objects, design vehicles and machines, and navigate vehicles and aircraft. They are also crucial in studying the stability and control of a rotating body.

### Similar threads

• Mechanics
Replies
20
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Mechanics
Replies
10
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Mechanics
Replies
1
Views
1K
• Mechanics
Replies
5
Views
5K
• Other Physics Topics
Replies
1
Views
1K
• Advanced Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
2K