Dario, a prep cook at an italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. the salad spinner rotates 6.00 more times before it comes to rest. assume that the spinner slows down with constant angular acceleration. part a what is the magnitude of the angular acceleration of the salad spinner as it slows down?

For an uniformly accelerated motion, the following relationship is used:

(1)

where a is the acceleration, S the distance covered, and vf and vi the final and initial speeds of the motion.

In our problem we are dealing with a rotational motion. Initially, the salad spinner has constant angular speed, which is given by

where f is the rotational frequency, which is the number of revolutions per second:

so the initial angular speed is

Then, the salad spinner starts to decelerate with constant deceleration , and during its deceleration it spins for other 6 revolutions, so covering a total angle of

until it stops, so until it reaches a final speed of .

To find the angular acceleration, we can use the equivalent of equation (1) for angular motions:

and so, since the final speed is :

where the negative sign means the salad spinner is decelerating.