Rotational Dynamics problem with instantaneous frame of reference

[YK0001]

Homework Statement

The wheel rolls without slipping such that at the instance shown, it has the angular velocity $\omega$ and angular acceleration $\alpha$. Determine the velocity and acceleration of point B on the rod at this instant. [![The image that shows the frame][1]]

[1[https://imgur.com/a/zRjzbDA]]

Relevant Equations

$$
v_B = v_A + \omega_{BA} \times r_{B/A}\newline ~~~
v_A = \omega r_{A/IC}\newline ~~~
a_B = a_A + \alpha_{BA} \times r_{B/A} + \omega \times (\omega \times r_{B/A})
$$

 

[phinds]

Is there a question in there somewhere? Are we supposed to check your work?

When you ask someone for a favor, such as checking your work, it is exceptionally bad form to make it hard for them by posting your work sideways and in sloppily hand written form.

Just sayin'.

 

[YK0001]

Is there a question in there somewhere? Are we supposed to check your work?

When you ask someone for a favor, such as checking your work, it is exceptionally bad form to make it hard for them by posting your work sideways and in sloppily hand written form.

Just sayin'.

Hi phinds,

Thank you for your response. I appreciate your feedback. I apologize if my post was unclear. I am not asking for someone to check my work for errors. I am aware that my solution is incorrect because it does not match the answer key. I am simply requesting guidance on how to solve this type of problem so that I can understand the correct approach for similar problems in the future.

Thank you for your understanding.

 

[kuruman]

I am simply requesting guidance on how to solve this type of problem so that I can understand the correct approach for similar problems in the future.

Before writing down any equations you need a strategy. It is very difficult to understand your strategy, which you say gave the wrong answer, from what you have posted. It may be that you have the correct approach but you went astray somewhere along its implementation. So how about describing with words how you propose to approach this problem? Then provide any equation that you may think is relevant to this strategy. When you do that, please show some consideration to those who are trying to help you and proofread your reply before posting it. Do not show equations that are cut in half or pictures that are sideways.

 

[Lnewqban]

Welcome. @YK0001 !

Consider that point A has an instantaneous velocity that can be considered as two components: one horizontal (same as velocity of point O) and another vertical (tangential).
Consider that point B has an instantaneous velocity which direction is constrained to be only horizontal.
Therefore, the A-B link is simultaneously experimenting a rotation and a translation respect to the ground.

 

[berkeman]

I have been working with @YK0001 on LaTeX, so hopefully any follow-up posts by them should use LaTeX.

 

[kuruman]

Question to OP:
When is "this instant"? In the figure it appears that point A is at the 9 o'clock position. Is that correct?