I found the correct alpha.
I then attempted to find the correct values for the acceleration of point P at the instant described.
I am having difficulties with the velocity and the accelerations relative for my equations.
I believe that both the acceleration and velocioties relative are point P as observed from point O, is this right?
I then try to continue my calculations, using that the speed of P is related to the angular velocity and its distance from its axis. I then go onto use this in my calculation for the acceleration (which is fully in the negative k direction).
So, my real question is, what is V_rel and A_rel? Is it the velocity and the acceleration from an observer at O or some other location?
~Joel
4 comments:
Points O and P are on the same rigid body, so Vrel and Arel are 0.
I am having a problem with this question and dont exactly know where i am going wrong. I get the correct alpha value, but the acceleration value for P is not right. I am correct in assuming that I can use a_P=a_O+alpha X r_P/O - w^2*r_P/O right?
Please note that the acceleration equation has the general form of:
a_P = a_O + alpha x r_P/O + (a_P/O)_rel + 2 omega x (v_P/O)_rel + omega x (omega x r_P/O).
As Emily says above, the third and fourth terms on the RHS of this equation are zero (in agreement with your equation also). However, your last term on the RHS is not correct.
[Note that when r_P/O is in a plane that is perpendicular to the omega vector, the last term on the RHS of the above equation reduces that what you wrote down. This is what we used back in Chapter 5 when we looked at motion in a single plane. For this 3D problems, like 7/10, you must use the full form of omega x (omega x r), not -omega^2*r.]
Does this make sense?
yes thank you
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