Maximizing Rotary Projectile Motion: Finding Distance and Path Diameter

[elmariachi]

Hi all,
the problem i have is that there is a rotating disk with nozzles on its circumference. a material is being pushed into this rotating disk/plate and its being released from the nozzles tangentially. The disk is rotating with a certain rpm such that the angular velocity of the particle just leaving the disk is w*r.
I believe that the particle from the disk will follow a circular path in the direction of the rotating disk. The rotating disk is enclosed within a room of specified length with air blown from the bottom of this enclosure such that the air resists the particles coming out of the disk.
I wanted to make sure that the particles thrown out of the disk don't go and hit the walls of the enclosure.I want to know, how can I find the longest horizontal distance , the material will travel just after leaving the disk and How big a circular path will it take (diameter).I will appreciate the help.

thanks

 

[abercrombiems02]

You need to start this problem defining two sets of unit vectors, a set that is inertially fixed and a set that is fixed to the rotating disc. In this case if we are in a horizontal plane we can neglect the effects of gravity since this disc is just traveling on the horizontal surface. I've done this problem with a rod in which there was one thruster and one end always thrusting tangential to linear velocity of the tip. If you apply F = ma, the only force you have acting is the thrust in the tangential direction. However, in your case you have a disc so there may be multiple forces, but note that if you have symmetry in these forces the disc will only rotate because while the net moment is non-zero, the net force will be zero. If you are familiar with SIMULINK i can send you my .mdl file so you can get an idea of how your EOMs should look.

Ooops forgot to add that you will also need to apply a moment equation to find a state equation for theta (or whatever you use for your angular measurement).

Unfortunately in the end you should end up with a set of non-linear DE's :(