Question

find the linear speed v of the tip of the minute hand of a clock, if the hand is 2 cm long. v = cm per minute (simplify your answer. type an exact answer, using π as needed. use integers or fractions)

Explanation:

Step1: Determine the distance traveled in one - hour

The minute - hand of a clock makes a full circle (circumference) in 60 minutes. The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 2$ cm, so $C=2\pi\times2 = 4\pi$ cm.

Step2: Calculate the linear speed

The linear speed $v$ is the distance traveled divided by the time taken. The time taken for one full - circle is $t = 60$ minutes. So $v=\frac{4\pi}{60}=\frac{\pi}{15}$ cm per minute.

Answer:

$\frac{\pi}{15}$