Question

example 5: the second hand of a clock is 10.2 cm long. find the linear speed of the tip of the second hand in cm/s.

Explanation:

Step1: Find the circumference

The second - hand moves in a circle. The formula for the circumference of a circle is $C = 2\pi r$. Here, $r = 10.2$ cm, so $C=2\pi\times10.2 = 20.4\pi$ cm.

Step2: Determine the time period

The second - hand makes one full revolution in 60 seconds.

Step3: Calculate the linear speed

The linear speed $v=\frac{d}{t}$, where $d$ is the distance traveled and $t$ is the time. Here, $d = C = 20.4\pi$ cm and $t = 60$ s. So $v=\frac{20.4\pi}{60}=\frac{20.4\pi}{60}\approx\frac{20.4\times3.14}{60}=\frac{64.056}{60}=1.0676$ cm/s.

Answer:

$1.0676$ cm/s