Posted by T.Gracken on August 30, 2002 at 11:50:07:
In Reply to: angular velocity posted by Ryan on August 30, 2002 at 08:30:31:
: This is not a homework problem so please do not give me the answer- I just want a push in the right direction.
: Problem: I have some partical "P" moving along the line x=a at a constant velocity "v". The diagram shows point P in the first quadrant with a right triangle connecting the orgin "point "o", (a,0), and (a,p). The height p is labeled Y.
: I am looking to find the angular velocity and angular acceleration.
: I know that the angular distance is some fraction of the perimeter --> (dist op) * Theta
: and the distance OP would equal sqrt(y^2 + a^2)
: and theta would equal arcsin of y/OP or some other inverse trig.
: ----> Am I on the right track? I am asking because I feel like I am not using the constant velocity "v" in my setup.
If I understand you correctly, you have a point moving vertically (on a line x=a) at a constant velocity and you want to know how fast the angle formed by the x-axis and the line connecting the origin to the point is changing.
you might want to consider setting up a function where T (theta), is the angle. then the triangle formed will have adjacent side equal to a and let y = opposite side length (this position will be determined by the velocity of the point).
or t = arctan(y/a)
then dT/dy (derivative of T with respect to y) will give angular velocity
and d2T/dt2 (second derivative) will give agular acceleration.
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