Exploring Velocity/Acceleration with Pi

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In summary: The equation for a spiral is ##r = \theta##, where ##r## is the radius of the spiral, ##\theta## is the angle of the spiral, and ##r_0## is the starting radius.
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stidiek
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Imagine a compass that can move in two ways: 1- Opening it to make a Radius 2- Draw a circle. If we can imagine it going at the same velocity (or accelaration), can we create a phormula of velocity and aceleration base on Pi... and see what it implies?
Imagine a compass that can move in two ways: 1- Opening it to make a Radius 2- Draw a circle. If we can imagine it going at the same velocity (or accelaration), can we create a phormula of velocity and aceleration base on Pi... and see what it implies?
 
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  • #2
stidiek said:
Imagine a compass that can move in two ways: 1- Opening it to make a Radius 2- Draw a circle. If we can imagine it going at the same velocity (or accelaration), can we create a phormula of velocity and aceleration base on Pi... and see what it implies?
This is somewhat confused. If you're talking about the "velocity" at which the legs open, you need to describe that motion in terms of how many degrees or radians per second/minute/whatever the angle changes. You would also need to describe the rate at which the moving leg moves, either in inches/cm/whatever per second/minute/whatever or in terms of the rate of change of angle, relative to some fixed direction.

In any case, if one leg of the compass is moving outward, that leg will trace out a spiral, which does have a formula, but the formula doesn't have anything to do with the number ##\pi##.

In polar coordinates, the equation ##r = \theta## represents a spiral.
 
  • #3
Hi, I think you get the idea behind it. We already had velocity and acceleration phormulas, but I'm proposing to imagine a fixed velocity in both movements of the compass, then, given that, Pi can be seen in terms of acceleration. Gravity and Pi are related in relativity phormulas, pendulum... etc... so I guess I'm just pointing to a previously searched region of questions... but maybe it's a refreshing thought.
 
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242879
 
  • #5
stidiek said:
... but maybe it's a refreshing thought.
I'm afraid you're a couple of thousands years late. And its path length is known since 1670.
 
  • #6
I know that Pi has a value (incomplete)... Can we just talk about its relation with the acceleration (?)
 
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Thread closed.
There is no relationship between ##\pi## and your scenario with the compass.
 

Related to Exploring Velocity/Acceleration with Pi

1. What is the relationship between velocity and acceleration?

The relationship between velocity and acceleration is that acceleration is the rate of change of velocity over time. In other words, acceleration measures how quickly an object's velocity is changing.

2. How is Pi used in exploring velocity and acceleration?

Pi, or the mathematical constant π, is often used in equations that involve circles or circular motion. Since velocity and acceleration can be represented as vectors, which have both magnitude and direction, they can be thought of as moving along a circular path. Therefore, Pi is often used in the equations that describe these motions.

3. What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement of an object divided by the total time taken. It gives an overall measure of an object's velocity over a certain period of time. Instantaneous velocity, on the other hand, is the velocity of an object at a specific moment in time. It is calculated by finding the slope of the tangent line to the object's position-time graph at that point.

4. How does acceleration affect an object's motion?

Acceleration affects an object's motion by changing its velocity. If an object is accelerating, its velocity is changing, either by speeding up, slowing down, or changing direction. The greater the acceleration, the greater the change in velocity and therefore the greater the effect on the object's motion.

5. How can Pi be used to calculate an object's acceleration?

Pi can be used in the equation for centripetal acceleration, which is the acceleration of an object moving in a circular path. The equation is a = v^2/r, where a is acceleration, v is velocity, and r is the radius of the circular path. Since Pi is used in the calculation of the circumference of a circle, it is also used in the calculation of centripetal acceleration.

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