A rolling (and accelerating?) wheel

Description : A wheel is going to start at the origin (with a point P on the top of the wheel if theta=0 when t=0). It can have an intial angular position/velocity/acceleration (note, this would the same as saying the center of the wheel had an initial linear position/velocity/acceleration). We confine ourselves to a quadratic relationship between the angle theta and time :
                                        theta = theta0 + omega0*t + ½*alpha*t2
The angle theta is positive in a clockwise sense. The angle is measured out from the center of the circle, and points to a point P on the circle (indicated in the animation). The vectors coming out of the red point P are the blue instantaneous velocity vector (scaled down by a factor of 4), and the green instantaneous acceleration vector (scaled down by a factor of 20). You can change the various values below, and then click the Update Information button, and then the PLAY button to run the animation.

Initial conditions :

  • Initial angle (theta0) of point P  radians
  • Initial anglular velocity of the circle  rad/s
  • Angular acceleration of the circle  rad/s/s

Horizontal plotting constraints :
Variable plotted : time    Theta    Theta/Pi    X
Autoscale Horizontal or
My scale : HorMin =   HorMin =

Vertical plotting constraints :
Variable plotted : Y    |V|    Vx    Vy    |A|
Autoscale Vertical or
My scale : VerMin =   VerMin =

(The animation may move off screen, but the graph will go until you stop it.)

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