Question

What is the angular velocity of the minute hand on a clock?

Answer 1

Hint: The angular velocity can be defined as the rate of the angular position of the rotating body. The rate of the rotation around an axis is usually expressed in the radians or the revolutions per second or per minute.

Formula used:
Angular velocity can be expressed as –
$\omega = \dfrac{{\Delta \theta }}{{\Delta t}}$
Here $\omega $ is the angular velocity, $\Delta \theta $ is the change in the angular rotation and $\Delta t$ is the change in the time

Complete step by step answer:
Minute hand of the clock rotates by $2\pi $ radians in every one hour. Therefore, time taken by a minute hand is one hour. We know that, $t = 1{\text{ hr = 3600s}}$. Now, the angular velocity can be given as –
$\omega = \dfrac{\theta }{t}$
Placing the values in the above expression –
$\omega = \dfrac{{2\pi }}{{3600}}$
Find the factors for the term in the denominator.
$\omega = \dfrac{{2\pi }}{{2 \times 1800}}$
Common factors from the numerator and the denominator cancels each other. Therefore remove from the numerator and the denominator.
$\therefore \omega = \dfrac{\pi }{{1800}}\,rad/s$

Hence, the angular velocity of the minute hand on a clock is $\dfrac{\pi }{{1800}}\,rad/s$.

Note: Remember the angular velocity is also known as angular frequency vector is the vector measure of the rotation rate which refers to how fast an object rotates or resolves with relative to another point. Do not forget to write the specific unit to the resultant value.