How to Rank Radial Acceleration Magnitudes from Angular Velocity Graph?

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SUMMARY

The discussion centers on ranking the radial acceleration magnitudes for a rotating disk based on its angular velocity graph. The correct ranking of the instants a, b, c, and d according to radial acceleration is c > a > b = d. The confusion arose from misinterpreting angular acceleration as the primary factor instead of understanding that radial acceleration is dependent on both angular velocity and the radius of the disk. The key equation involved is α = dω/dt, which relates angular acceleration to the change in angular velocity over time.

PREREQUISITES
  • Understanding of radial acceleration in rotational motion
  • Familiarity with angular velocity and its graphical representation
  • Knowledge of angular acceleration and its calculation
  • Basic principles of rotational dynamics
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  • Learn how to derive radial acceleration from angular velocity graphs
  • Explore the implications of angular acceleration in rotational motion
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Homework Statement


Figure 10-22 is a graph of the angular velocity versus time for the rotating disk of Fig. 10-21a.
11_23.gif


For a point on the disk rim, rank the instants a, b, c, and d according to the magnitude of the radial acceleration, greatest first (use only the symbols > or =, for example b=d>a>c).

Homework Equations


\alpha = d\omega/dt


The Attempt at a Solution


I figured that the angular acceleration is just the slope of the angular velocity graph, so the magnitudes from greatest to least would be c>a>b=d.

What did I do wrong? The site says that I am wrong.
 

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Hi keemosabi! :smile:

Read the question! :rolleyes:
keemosabi said:
Figure 10-22 is a graph of the angular velocity versus time for the rotating disk …
For a point on the disk rim, rank the instants a, b, c, and d according to the magnitude of the radial acceleration …

I figured that the angular acceleration …

angular?
 

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