Question

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what is the average angular velocity of the seconds hand of a clock?
$omega = 0.10 rad/s$
$omega = 0$
$omega = -0.10 rad/s$
$omega = -2 pi rad/s$
$omega = 2 pi rad/s$
the initial angular velocity of a ceiling fan is 6.28 rad/s. it accelerates uniformly to 3.14 rad/s acceleration?
$0.39 rad/s^{2}$
$-0.79 rad/s^{2}$

Explanation:

Step1: Determine the angular displacement and time period

The seconds - hand of a clock makes one full revolution (\(\Delta\theta=- 2\pi\) rad, negative because it rotates clock - wise) in \(T = 60\) s.
The formula for average angular velocity is \(\omega=\frac{\Delta\theta}{\Delta t}\).

Step2: Calculate the average angular velocity

Substitute \(\Delta\theta=-2\pi\) rad and \(\Delta t = 60\) s into the formula:
\(\omega=\frac{-2\pi}{60}\approx - 0.10\) rad/s.

Answer:

\(\omega=-0.10\) rad/s (the third option).