Measuring Centripetal Acceleration Geometrically

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Discussion Overview

The discussion revolves around the measurement of centripetal acceleration using geometric methods, specifically without relying on force measurements or traditional parameters like radius and period. Participants explore the implications of measuring acceleration in a circular motion context and the challenges associated with such measurements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Scott questions whether centripetal acceleration can be measured using just a ruler, without needing to find radius or period, and references a concept involving rotating frames.
  • Zz suggests illustrating the concept using linear motion to clarify the approach Scott is considering.
  • A participant emphasizes that acceleration is defined as a change in velocity and questions how one can measure acceleration without units of measurement.
  • Scott reiterates the initial question and provides a method involving a Cartesian coordinate system to measure the object's position over time, leading to the calculation of acceleration vectors.
  • Scott expresses appreciation for the clarification provided by prevect regarding the definition of acceleration.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints and does not reach a consensus on the feasibility of measuring centripetal acceleration geometrically without traditional parameters. Participants express confusion and seek clarification on the concepts involved.

Contextual Notes

There are limitations regarding the assumptions made about the measurement setup, such as the need for multiple rulers if measuring in a plane, and the dependence on the definitions of acceleration in different contexts.

Who May Find This Useful

This discussion may be of interest to those exploring experimental methods in physics, particularly in the context of circular motion and acceleration measurements.

scott_alexsk
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Is there a way to measure centripetal acceleration independent of a force measurement? If I had just a ruler, and a ball was rolling along a circular path, could I 'measure' the centripetal acceleration itself, without resorting to finding the radius, period, etc. Someone once told me that this is a special case of acceleration, with rotating frames, but then what does the acceleration mean, in the rate of change of the angle of inclination of the frame?

Thanks,
-Scott
 
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This is a bit confusing.

Maybe you can illustrate what you mean by doing this with linear motion and demonstrate what you wanted to do with the regular linear acceleration, presuming that what you want to do is clear with this case.

Zz.
 
v^2 / r How can you measure something without units of measurement? Acceleration is a change in the velocity. Acceleration is there because there is a change in direction in circular motion.
 
scott_alexsk said:
Is there a way to measure centripetal acceleration independent of a force measurement? If I had just a ruler, and a ball was rolling along a circular path, could I 'measure' the centripetal acceleration itself, without resorting to finding the radius, period, etc. Someone once told me that this is a special case of acceleration, with rotating frames, but then what does the acceleration mean, in the rate of change of the angle of inclination of the frame?

Thanks,
-Scott

I assume you're interested in the Newtonian case.

For convenience, set up a Cartesian coordinate system (x,y,z).

Measure x(t), y(t), and z(t), the position of the object as a function of time.

The object's acceleration vector will then be d^2 x / dt^2, d^2 y/ dt^2, d^2 z / dt^2. (This works for any path, including a circular one).

The magnitude of this vector will be the total acceleration.

Note that you'll need at least two rulers if the ball is on a plane, i.e. you'll need to measure x and y.
 
Thank you prevect. That is a very useful (and simple) definition.

-Scott
 

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