# Angluar Velocity and Revolutions

## Homework Statement

You switch a food blender from its high to its low setting; the blade speed drops from 3100 rpm to 1300 rpm in 2.1 s. How many revolutions does it make during this time?

## Homework Equations

$$\omega$$i = $$\frac{3100 rpm * (2 * pi)}{60}$$ = 324.6 rad/sec
$$\omega$$f = $$\frac{1300 rpm * (2 * pi)}{60}$$ = 136.1 rad/sec

$$\omega$$f = $$\omega$$i + $$\alpha$$t

$$\omega$$f$$^{2}$$ = $$\omega$$i$$^{2}$$ + 2$$\alpha$$($$\Delta$$$$\Theta$$)

## The Attempt at a Solution

136.1 = 324.6 + 2.1 $$\alpha$$

$$\alpha$$ = 89.8 rad/sec$$^{2}$$

136.1$$^{2}$$ = 324.4$$^{2}$$ + 2 * 89 ($$\Delta$$$$\Theta$$)

($$\Delta$$$$\Theta$$) = 482.8 rad / (2 * pi) = 76.8 rev

Want to make sure if this is correct.