Question

The time it takes a spinner to stop completely is 12 seconds. If the spinner completes 6 revolutions in this time, what was the average angular velocity of the spinner, in radians per second, for the 12-second interval?

Answer 1

3.14 rad/s is the average angular velocity of the spinner.

Explanation:

Average angular velocity :

`\omega=(\Delta \theta )/(\Delta t)`

Change in angular displacement Δθ= 6 revolutions

1 revolution = 360°

6 revolutions = 6 × 360° = 2160° = 37.70 rad

(1°= 0.0174533 radians )

Change in time Δt= 12 s

Average angular velocity of the spinner =

`=(37.70 rad)/(12 s)=3.14 rad/s`

3.14 rad/s is the average angular velocity of the spinner.

Answer 2

The angular velocity by definition is given by:
w = rev / t
Where:
rev: revolutions
t: time
Substituting values we have:
w = (6 * (2 * pi)) / (12)
w = 3.141592654 rad / s
Answer:
the average angular velocity of the spinner, in radians per second, for the 12-second interval is:
w = 3.141592654 rad / s