Solving Constant Angular Velocity Homework: Pin Velocity & Acceleration

[limenuke]

Homework Statement

Given the above diagram and that the arm R swings at a constant angular velocity theta dot (dtheta/dt), we are to solve for the velocity of the pin and the acceleration of the pin.

Homework Equations

h= (theta dot)*r^2
dtheta/dt = v
v= (theta dot) * dr/dt

The Attempt at a Solution

I've been struggling with these questions since they seem the easiest to do in polar but our professor has been working more specifically in cartesian. Our textbook doesn't seem to like using polar either so at the moment, I'm having a lot of trouble coming up with applicable formulas.

For velocity, I tried the above forumla...

dr/dt = dr/dtheta * dtheta/dt (chain rule)
sub in dtheta/dt =h/r^2
sub in dr/dt = v
sub in dr/dtheta = -Rsin theta since the circular arc traces part of the curve r= R cos theta

v = (-Rsin theta) (h/r^2)

Since they're asking for velocity, the only thing I put down to indicate a direction was unit vector e sub t where e sub t is the tangential component of arc DE. I've no idea if this answer is acceptable.

For acceleration, I have no idea where to start.
I just can't seem to know where to start. It would be helpful if someone could provide formulas or point me in the right direction. I'm looking for advice, not answers (yet).

Thanks!

 

[anathema]

Hello,

Thank you for your post. It seems like you have already made some progress in solving for the velocity of the pin. Your approach using polar coordinates is correct, and using the chain rule was a good idea. However, there are a few things that need to be corrected in your solution.

First, the formula you used for velocity (v= theta dot * dr/dt) is not correct. This formula applies to linear motion, but in this case, we are dealing with rotational motion. Therefore, we need to use the formula v= r * theta dot, where r is the distance from the center of rotation to the point of interest (in this case, the pin). So, the correct formula for velocity in this case is v= R * theta dot.

Secondly, the unit vector e sub t you mentioned is not necessary to indicate the direction of the velocity. The direction of the velocity can be determined by the direction of the angular velocity (theta dot). In this case, since the arm R is swinging in a counterclockwise direction, the velocity of the pin will also be in a counterclockwise direction.

Now, for the acceleration, we can use the formula a= r * alpha, where alpha is the angular acceleration. Since the arm R is swinging at a constant angular velocity, the angular acceleration is zero. Therefore, the acceleration of the pin will also be zero.

I hope this helps. Let me know if you have any further questions or need clarification. Good luck with your homework!