Question

The angular velocity of the second hand of a clock is

Answer 1

Step 1. Angular velocity:

1. Angular velocity may be defined as the rate of change of the position angle of an object with respect to time.
2. It is less common than linear velocity since it only concerns objects that are moving along a circular path.
3. For example, a roulette ball on a roulette wheel, a race car on a circular path, and a Ferris wheel are all examples of angular velocity.
4. The unit of angular velocity is $\raisebox{1ex}{$rad$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$.

Step 2. Formula used:

Mathematically,

$\omega =\frac{\theta }{t}$ …………….$\left(1\right)$

where $\omega$ = angular velocity, $\theta$ = position angle, and $t$ = time.

Step 3. Calculations:

Now, the Seconds hand of the clock takes $60$ seconds to cover one cycle of $2\mathrm{\pi }$ radian.

Putting the values in the equation $\left(1\right)$

Thus, $\omega =\frac{2\mathrm{\pi }}{60}=\frac{\mathrm{\pi }}{30}\raisebox{1ex}{$rad$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Hence, the angular velocity of the second hand of a clock is $\frac{\mathrm{\pi }}{30}\raisebox{1ex}{$rad$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$.