How Does Distance r Influence Angular Velocity in Rigid Body Dynamics?

[ruzfactor]

Need help! Rigid Body Dynamics

Homework Statement

I'm having problem with the following problem. The encircled portion of the figure is giving me trouble. I am getting confused on how to correlate it with reference frame oxyz. please help. It's urgent.. :(

what is the significance of distance r for calculating angular velocity of the reference axis oxyz?


I need to find out the components of the absolute acceleration of O along ox,oy& oz.

Please view the Attachment.

Homework Equations

equation of absolute acceleration and velocity to be used.

The Attempt at a Solution

I'm stuck on the first question. Because I'm confused whether the r has any significance in the solution for the first question.

 

[KataKoniK]

I also don't know how to relate the encircled portion with the reference frame oxyz.

Dear student,

I understand your confusion and I am here to help you with your problem. Let us start by understanding the concept of rigid body dynamics. A rigid body is a body that does not deform under the action of external forces. In other words, the distance between any two points on the body remains constant. This means that the body can be treated as a single entity and its motion can be described by the motion of its center of mass.

Now, coming to your first question, the distance r is significant because it represents the distance between the point O and the reference frame oxyz. This distance is important because it determines the position of the point O with respect to the reference frame and hence, it affects the calculation of the angular velocity of the reference axis oxyz. The angular velocity is defined as the rate of change of angular displacement, and it is calculated by dividing the linear velocity by the distance r.

Moving on to the second question, in order to find the components of the absolute acceleration of O along ox, oy, and oz, we need to use the equations of absolute acceleration and velocity. These equations involve the angular acceleration and velocity, which can be calculated using the angular velocity of the reference axis oxyz. Once we have the angular acceleration and velocity, we can use them to find the absolute acceleration and velocity of O along ox, oy, and oz.

I hope this helps you to understand the problem better. If you still have any doubts, please feel free to ask. Remember, it is important to understand the concept first before attempting to solve the problem. Good luck with your homework!