Calculating Angular Speed: Simple or Complicated?

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Homework Help Overview

The discussion revolves around calculating the instantaneous angular speed of a wheel that accelerates from rest with a given linear acceleration. Participants are exploring the relationship between linear and angular quantities in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the appropriateness of using linear acceleration to derive angular acceleration. There is an attempt to connect linear formulas to angular motion, and some participants express uncertainty about the correct application of these concepts.

Discussion Status

The discussion is active, with participants raising questions about the definitions and relationships between linear and angular quantities. Some guidance has been offered regarding the relationship between linear acceleration and angular acceleration, but no consensus has been reached on the correct approach.

Contextual Notes

There is a noted confusion regarding the use of linear acceleration in the context of angular motion, and participants are working with the assumption that they need to relate these two types of acceleration without clear definitions or formulas provided.

angel_romano
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If a wheel accelerates from rest at 1.0 m/s^2 and I need to find the instantaneous angular speed of the wheel at .10s would this be the proper formula:

final angular speed=initial angular speed + angular acceleration(change in time)

When I use this formula, it comes out to .10 rad/s which just seems to simple.
 
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Well, you state the wheel accelerates from rest at 1.0m/s^2. m/s^2 is a measurement of linear acceleration not angular acceleration.
 
But how does the angular acceleration fit in then?

I have linear formulas, but I'm not sure which one I would use.
 
[tex]\alpha r = a[/tex]
 
With a little bit of reasoning one could solve it with basic knowledge...
Via the linear acceleration one could calculate the linear velocity of the centre of the wheel after the given time. At this stage one could reason that the Earth is moving with the same speed in the opposite direction while the wheel is standing still, hence the speed of rotation of the wheel since it is in contact with the earth.
 

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