Coriolis Acceleration of a Mechanism

[ConnorM]

Homework Statement

Rod AB rotates with the angular velocity and acceleration CCW as shown. Points A and D are pin connected. The collar C is pin connected to the link CD and slides over the link AB. At the instant shown the link CD is vertical and the link AB has an angular velocity of 2 rad/s, and an angular acceleration of 4 rad/s²

determine,

1) The angular velocity of link CD
2) The relative velocity of point C with reference to A
3) The velocity of point C
4) The angular acceleration of link CD
5) The relative acceleration of point C with reference to A
6) The acceleration of point C

http://imgur.com/6lTfnYV --> Here is a picture of the question so you can see what the mechanism looks like.

Homework Equations

v = ωr (1)
a_n = ω²r (2)
a_t = αr (3)
v_b = v_a + v_b/a (4)
a_b = a_a + a_b/a (5)[/B]

Coriolis Accel. eqn

a_corn = -2ω(v_{b/a t}) (6)
a_cort = 2ω(v_{b/a n}) (7)

The Attempt at a Solution

Since this solution involves drawing various vectors I will include a picture of my work to help make things a bit easier. All of my work is in this picture as well so you can either look at my work their or at what I have written below. http://imgur.com/PAjUJoh,4PSWKHt

VELOCITY ANALYSIS

First off I started with the velocity analysis and drew where I thought the velocity vectors of each point would be. From my vectors v_c, v_c', and v_c/c' I found,

v_c' = v_c cos 30 = 1.386 m/s
v_c/c' = v_c sin 30 = 0.8 m/s

next I found my angular velocity of CD,

ω_CD = v_c' / r_CD = 4.62 rad/s

ACCELERATION ANALYSIS

I started off by writing down all the relevant equations

a_cn = r_AC ω_AC²
a_ct = r_AC α_AC

a_c'n = r_CD ω_CD²
a_c't = r_CD α_CD

a_c/c'n = ?
a_c/c't = ?

a_corn = -2ω_CD(v_c/c'n)
a_cort = 2ω_CD(v_c/c't)

What I am stuck on is that I don't know where my vectors are supposed to go. I'm not sure what I've done wrong and don't really know where to go from here.

 

[mfb]

The ω^2-related accelerations are always towards the center of rotation, the others orthogonal to it. And you know the orientations of those vectors with your 30°-sketch, this is similar to the velocities.

 

[ConnorM]

The ω^2-related accelerations are always towards the center of rotation, the others orthogonal to it. And you know the orientations of those vectors with your 30°-sketch, this is similar to the velocities.

So since I drew my v_c/c' directly down my a_c/c'n would be down in the same direction and I would have no tangential a_c/c't?

 

[mfb]

I'm not sure if I understand your notation (why don't you use coordinates like x and y?). You have both horizontal and vertical acceleration at point C.

 

[ConnorM]

It's ok I think I have found what I did wrong!