Question

What is the angular speed of the minute hand of a clock? If the minute hand is 5 cm long. What is the linear speed of its tip?

Answer 1

Step 1: Given information

Radius of the minute hand, $\mathrm{R}=5\mathrm{cm}$$=5\times {10}^{-2}\mathrm{m}$

Time taken to complete one rotation, $\mathrm{T}=1\mathrm{hr}$$=3600\mathrm{s}$

Step 2: To find

1. The angular speed of the minute hand of a clock.
2. The linear speed of its tip.

Step 3: Finding the angular speed of the minute hand of a clock

We know the formula,

Angular speed $\mathrm{\omega }=\frac{2\mathrm{\pi }}{\mathrm{T}}$

By substituting the given values,

$$\begin{gathered} \mathrm{\omega }=\frac{2\mathrm{x}3.14}{3600} \\ =1.74\times {10}^{-3}\mathrm{rad}/\mathrm{s} \end{gathered}$$

Step 4: Finding the linear speed of its tip

We know the formula,

$\mathrm{v}=\mathrm{r\omega }$

By substituting the values, we get

$$\begin{gathered} \mathrm{v}=5\times {10}^{-2}\times 1.74\times {10}^{-3} \\ =8.7\times {10}^{-5}\mathrm{m}/\mathrm{s} \end{gathered}$$

Therefore, the angular speed is $1.74\times {10}^{-3}\mathrm{rad}/\mathrm{s}$ and the linear speed is $8.7\times {10}^{-5}\mathrm{m}/\mathrm{s}$.