Determine the Velocity and Acceleration of the Rotating Rod

[Northbysouth]

Homework Statement

The body is formed of slender rod and rotates about a fixed axis through point O with the indicated angular properties. If ω = 4.6 rad/s and α = 4.4 rad/s², determine the instantaneous velocity and acceleration of point A.

I have attached an image of the question

Homework Equations

v = wXr

a = αXr + wX(wXr)

The Attempt at a Solution

r = <0.5sin(24)i + 0.23cos(24)i +0.5cos(24)j - 0.23sin(24)j>

r = <0.4135i + 0.3632j + 0k>

w = 4.6k

v_a = <0i + 0j + 4.6k> X <0.4135i + 0.3632j + 0k>

V_A = 1.6707i + 1.9021j

But it says this is wrong. What am I missing?

I know for the second part that I need to use:

a_A = αXr + wX(wXr) but I can't seem to get wXr right.

Any advice would be greatly appreciated.

 

[staysys]

well I see that you are using 0.23m as the distance from the straight part of the rod to the point A. However, I think 0.23m is the radius of the cirular part of the rod, so then the distance you should be using would be the diameter 0.46m.

 

[Northbysouth]

You are correct. Thank you. My final correct answers are:

V_A = 1.24i + 2.869j

a_A = -12.01i + 8.449j