3-Dimensional Projectile Motion

In summary, the conversation discusses the representation of coordinates in 2-dimensions, specifically the x and y coordinates. It also mentions using a different coordinate system for calculating the z coordinate when rotating around the y axis. The conversation also touches on the use of Cartesian coordinates and the six coordinates used to describe a spinning rigid body. The topic of kinetic energy is also brought up, particularly the lack of formulas that include rotation or orbital motion. Finally, the conversation briefly discusses the analysis of the angular kinetic energy of water leaving a sprinkler.
  • #1
amcavoy
665
0
I know in 2-dimensions, the x coordinate is represented by

[tex]x=v_{0}\cos{(\theta)}t,[/tex]

and the y coodinate is represented by

[tex]y=-\frac{1}{2}gt^2+v_{0}\sin{(\theta)}t+h.[/tex]

How would you calculuate the z coordinate if it was rotating around the y axis? For example; a sprinkler.

Thanks for your help.
 
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  • #2
alexmcavoy@gmail.com said:
I know in 2-dimensions, the x coordinate is represented by

[tex]x=v_{0}\cos{(\theta)}t,[/tex]

and the y coodinate is represented by

[tex]y=-\frac{1}{2}gt^2+v_{0}\sin{(\theta)}t+h.[/tex]

How would you calculuate the z coordinate if it was rotating around the y axis? For example; a sprinkler.

Thanks for your help.

I wouldn't use cartesian coordinates system if I were you...

Zz.
 
  • #3
Who's rotating??

Daniel.
 
  • #4
What would you use? Even if there was a better way, I am interested in how it would be defined in rec. coordinates.

Thanks again.
 
  • #5
Are u thinking of a spinning (finite size) projectile wondering through the (viscous,moving,nonisothermal,nonisobaric) atmosphere,in the nonconstant nonhomogenous gravitational field created by a rotating Earth??

Daniel.
 
  • #6
I'm thinking of no outside forces besides gravity.
 
  • #7
Anyway,a spinning rigid body is typically discribed by 6 coordinates:the 3 cartesian for the CM (parametrize the body's translation) and the 3 Euler angles (parametrize the body's rotations).

Daniel.
 
  • #8
Ok well, I haven't had a physics class before, so what I know is strictly what I have read out of a book (which isn't much). What type of physics class would I learn these types of things in?
 
  • #9
A college course in classical mechanics in Newtonian formulation.

Daniel.
 
  • #10
amcavoy said:
I'm thinking of no outside forces besides gravity.

I was also wondering why I can't find a formula for kinetic energy that INCLUDES motion such as rotation or even a variable orbit? I admit I haven't seen a classroom in 15yrs. So if anyone can update me?
 
  • #11
amcavoy said:
I know in 2-dimensions, the x coordinate is represented by

[tex]x=v_{0}\cos{(\theta)}t,[/tex]

and the y coodinate is represented by

[tex]y=-\frac{1}{2}gt^2+v_{0}\sin{(\theta)}t+h.[/tex]

How would you calculuate the z coordinate if it was rotating around the y axis? For example; a sprinkler.

Thanks for your help.


I'd love to hear your answer on this as I too was wondering why Newtons EK Kinetic Energy does not include rotating or orbital objects. Keep me posted? thanks MJL
 
  • #12
How about K = (1/2)Iw^2. Where K is the angular kinetic energy, I is the moment of inertia of the rotating object, and w, it should be omega, is the angular velocity.

If you are trying to analyze the angular kinetic energy of water that leaves a sprinkler I can help you out there. It is zero. Once it leaves the jets it goes in a straight line. If you want to analyze what happens to the water once it leaves the jets it is best done by getting its velocity at the moment it leaves. Then you reduce it to a two dimensional analysis using y = (1/2)at^2 + vtsin(theta) + c, and x = vcos(theta) + d. Where c and d are the initial y and x values and v is the initial velocity.

The energy analysis of the rotating sprinkler is a bit more complex. It all depends on the shape of it and its mass distribution. But from your question I believe that you wanted to analyze the water once it left the sprinkler, I may be wrong.
 

Related to 3-Dimensional Projectile Motion

What is 3-Dimensional Projectile Motion?

3-Dimensional Projectile Motion is the motion of an object that is moving in three dimensions, with both horizontal and vertical components. It follows the same principles as 2-dimensional projectile motion, but also takes into account the third dimension.

What factors affect the trajectory of a 3-Dimensional projectile?

The trajectory of a 3-Dimensional projectile is affected by the initial velocity, angle of launch, air resistance, and the force of gravity. These factors determine the shape and path of the projectile's motion.

How is the motion of a 3-Dimensional projectile calculated?

The motion of a 3-Dimensional projectile can be calculated using the equations of motion, which take into account the initial velocity, angle of launch, and acceleration due to gravity. These equations can be solved to determine the position, velocity, and acceleration of the projectile at any given time.

Is air resistance a significant factor in 3-Dimensional projectile motion?

In most cases, air resistance does have a significant impact on the motion of a 3-Dimensional projectile. However, in situations where the object is small or moving at high speeds, air resistance may be negligible.

How is 3-Dimensional projectile motion used in real life?

3-Dimensional projectile motion is used in various fields such as engineering, sports, and military applications. It is used to calculate the trajectory of objects such as missiles, projectiles, and sports equipment, and is also important in understanding the motion of objects in space.

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