Question

Calculate the angular speed of the second hand and hour hand of the clock?

Answer 1

Step 1:Finding the angular velocity of second hand:

For the second hand of the clock,

One complete revolution takes 60 seconds and the distance covered will be $2\mathrm{\pi r}$ where r is the radius of the clock and $\mathrm{\pi }=3.14$

Angular displacement in one revolution will be $2\pi .$

So the angular velocity($\omega$) will be given by,

$$\begin{gathered} \omega =\frac{2\mathrm{\pi }}{60}rad/s \\ \omega =\frac{\mathrm{\pi }}{30}rad/s=0.10rad/s \end{gathered}$$

Step 2: Finding the angular velocity of the hour hand:

For hour hand, it takes 12 hours for one complete revolution.

Angular displacement in one revolution will be $2\pi .$

$\omega =\frac{2\mathrm{\pi }}{60\times 60\times 12}=\frac{\mathrm{\pi }}{21600}=1.45\times {10}^{-4}rad/s.$

Hence, the angular speed of the second hand and hour hand of the clock will be 0.10 rad/s and $1.45\times {10}^{-4}rad/s$ respectively.