How to Rank Radial Acceleration Magnitudes from Angular Velocity Graph?

[keemosabi]

Homework Statement

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

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.

 

[tiny-tim]

Hi keemosabi!

Read the question!

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?

 

[kerimek]

Your approach is correct, but your ranking is incorrect. The correct ranking from greatest to least magnitude of radial acceleration is c>b=a>d. This is because the slope of the angular velocity graph is greatest at point c, followed by point b and a, and then point d. Since radial acceleration is directly proportional to angular acceleration, the same ranking applies for radial acceleration. Additionally, at point c and b, the angular acceleration is in the same direction as the radial acceleration, resulting in a greater magnitude. At points a and d, the angular acceleration is in the opposite direction as the radial acceleration, resulting in a smaller magnitude.