Calculating Longest Projectile Distance from Rotating Disk | Projectile Motion

[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. The disk is rotating with a certain rpm. I want to know, how can I find the longest horizontal distance , the material will travel just after leaving the disk. I believe that the particle from the disk will follow a circular path in the direction of the rotating disk. How big a circular path will it take ( diameter).I will appreciate the help.

thanks

 

[Lee]

If I'm understanding this problem correctly, basically you have a rotating disc with a set angular velocity, and then your pushing something into it and a 'nozzle' is pushing off the disc. If so then the 'thing' is going to move off tangential to the circle where it leaves, the speed of the object will be about w*r, then from that your creating a projectile motion question where your initial velocity in the x direction is w*r and your inital velocity in the y is 0, hopefully you'll be given S, and the rest should fall into place.

If I understand your question correctly.

 

[BobG]

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. The disk is rotating with a certain rpm. I want to know, how can I find the longest horizontal distance , the material will travel just after leaving the disk. I believe that the particle from the disk will follow a circular path in the direction of the rotating disk. How big a circular path will it take ( diameter).I will appreciate the help.

thanks

Lee gave you the key to the problem. The velocity of the material is equal to the angular velocity times the radius.

There's a few other things to consider, though.

Conceptually, you're off on what you're expecting. Each bit of material travels in a straight line tangential to the disk. Assuming each bit of material travels the same distance, you will end up with a circular pattern, since the nozzle has moved between one bit of material being released and the next. The fact that the material is moving tangent to the disk (instead of directly outward) makes a difference.

Your angular velocity has to be in radians per second. You have revolutions per minute (rpm). You need to convert your rpm to radians per second. One radian is equal to the length of the radius laid along the circumference. If you know how to find the circumference of a circle, you can convert from rpm to rad/sec.

You need to know how high your disk is above the ground. The material will travel at a constant horizontal speed. It will also undergo downward acceleration due to gravity.