Angular acceleration of rod using relative accelerations

[roldy]

Homework Statement

A collar at point B slides on a 4 kg uniform rod CD. Knowing that in the position shown, crank AB rotates with an angular velocity of 5 rad/s and an angular acceleration of 60 rad/s^2, both clockwise, determine the force exerted on rod CD by collar B.

Homework Equations

relative velocities
relative accelerations
mass moment of inertia for a bar

The Attempt at a Solution

The question here is that I'm confused on how this other site got the angular velocity of CD. I figured it out to be -5 rad/s. Is there anything that I'm doing wrong? I understand how they got it their way, but I would like to use the method of relative velocities and accelerations.
Here is what they had. The first post is me asking them how they got it, still no response.
http://answerboard.cramster.com/mechanical-engineering-topic-5-153328-0.aspx

Here's is my attempted work...
http://img217.imageshack.us/my.php?image=120ia0.jpg

 

[Jhero]

Thank you for your help!Hello,

Thank you for sharing your work and the link to the forum post. After reviewing your solution and the discussion on the forum, I can see where the confusion lies.

First, let's clarify the given information in the problem. The problem states that the collar at point B is sliding on the rod CD, and that the crank AB is rotating with an angular velocity of 5 rad/s and an angular acceleration of 60 rad/s^2, both clockwise. This means that the motion of the rod CD is completely dependent on the motion of the crank AB.

Now, let's look at your solution. You correctly identified the angular velocity of the rod CD to be -5 rad/s, but there is a mistake in your calculation of the relative acceleration. The relative acceleration between two points is the difference between the accelerations of those points. In this case, the acceleration of point B is the same as the acceleration of point A, since they are connected by the rigid crank AB. Therefore, the relative acceleration between points B and C is the difference between the acceleration of point C and the acceleration of point A. The acceleration of point C can be found using the formula a = r*α, where r is the distance from the axis of rotation to point C and α is the angular acceleration. Plugging in the given values, we get a = 0.4*60 = 24 m/s^2. The acceleration of point A is simply the centripetal acceleration, which can be found using the formula a = ω^2*r, where ω is the angular velocity and r is the distance from the axis of rotation to point A. Plugging in the given values, we get a = 5^2*0.2 = 5 m/s^2. Therefore, the relative acceleration between points B and C is 24 - 5 = 19 m/s^2.

Now, let's compare this to the solution given on the forum. The solution on the forum used the formula a = r*α to find the acceleration of point B, which is correct. However, they made a mistake in their calculation of the relative acceleration. They incorrectly assumed that the acceleration of point C is the same as the acceleration of point B, which is not true since the motion of point B is dependent on the motion of point A. Therefore, their calculation of the relative acceleration is incorrect.

In summary,