What is the Formula for Acceleration in Rotation?

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Discussion Overview

The discussion revolves around understanding the formula for acceleration experienced by a body on a rotating wheel, specifically focusing on the components of acceleration in the x, y, and z axes. Participants explore the relationship between frequency, radius, and acceleration in the context of rotational motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about calculating acceleration in multiple axes for a body on a wheel with a given radius and frequency.
  • Another participant suggests that the acceleration in rotation is centripetal and directed towards the center.
  • A participant mentions a formula involving frequency and distance but seeks clarification on how to express acceleration in the x, y, and z directions.
  • It is noted that instantaneous acceleration is the derivative of velocity and is always directed towards the center of rotation, raising questions about the definition of the problem and the chosen coordinate system.
  • One participant identifies the presence of normal reaction, centripetal acceleration, and angular acceleration above the plane.
  • A participant speculates on maximum acceleration conditions based on specific coordinate values, questioning the behavior of acceleration in the y direction.
  • Another participant corrects a previous claim about the formula, stating that the formula for acceleration is a = v^2 / radius, and discusses the implications of choosing a coordinate system that rotates with the wheel.
  • It is suggested that calculating the actual position after a certain time could allow for determining the x and y components of centripetal acceleration using Pythagorean principles.

Areas of Agreement / Disagreement

Participants express differing views on how to approach the calculation of acceleration in multiple axes, with no consensus on a single method or formula. The discussion remains unresolved regarding the best way to define the problem and calculate the desired components of acceleration.

Contextual Notes

Participants highlight the need for clearer definitions and assumptions regarding the coordinate system and the specific instant at which acceleration is to be calculated. There are unresolved mathematical steps related to the application of formulas in the context of rotation.

Branny12000
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Hi there,

I am confused. I want to work out the acceleration that a body placed on a wheel of radius 10 mm going at a frequency of 3Hz would experience in the x y and z axis. The equations for rotation don't make this clear. They just give me one basic equation for acceleration

Can you help me understand this
Bran
 
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Branny12000 said:
They just give me one basic equation for acceleration.
You mean centripetal acceleration? It's towards the center.
 
Im not sure I just have 2*pi*freq*distance but I want of course the acceleration in the x y and z directions
 
The instantaneous acceleration is the derivative of the change in velocity per unit time. It is always towards the centre of rotation. So the question, with respect to coordinates, is arbitrary unless you define the problem more clearly.

Ie. at what instant do you wish to know the acceleration, over which chosen layout of coordinates?
 
it has normal reaction, centripetal acceleration and angular acceleration above the plane
 
Well At x = A So I am guess that the maximum acceleration is 2*pi*freq*distance and in the Y axis it would be when x = A y = 0? so it wouldn't experience maximum acceleration in the y direction?
 
The formula you have stated is for velocity (if distance = radius).
The formula for acceleration is a = v^2 / radius.

If you mean A to be acceleration then, yes, the y component is zero, but technically this means you have chose a coordinate set which does not see the wheel as spinning (because the coordinate turn with the wheel) so frequency = 0 and so will the other results. That is why the term centripetal accelerationis used.

If set the initial position to y = 0, x = 5, with the origin at the centre of the wheel (for example)
you could then calculate the actual position after (t) seconds, and use some pythagorus to get x and y components of the magnitude of centripetal acceleration (that you calculated with the above formula).
 

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