Question

length of the minute hand of a clock is 10 cm. Calculate its speed?

Answer 1

Angular velocity =thita/time
360/60=6

Answer 2

Answer: $\bold{1.745 \times 10^{-4} \, \, m/s}$


This question relates the concepts of Angular Velocity and Linear Velocity.


The object under consideration is the minute hand of a clock. The minute hand goes around once every sixty minutes. That is, the minute hand covers an angle of $360^{\circ}$ or $2\pi \, \, radians$ in sixty minutes.


So, we can calculate the angular velocity of the minute hand of the clock:

$\omega = \frac{Angle \, \, covered}{Time \, \, taken} \\ \\ \implies \omega = \frac{2\pi \, \, rad}{60 \times 60 \, \, sec} \\ \\ \implies \omega = \frac{\pi}{1800} \, \, rad/sec$


Now, we have to calculate the linear speed of the tip of the minute hand. The tip of the minute hand is at a distance of 10 cm from the axis of the rotation. So we have:

$r = 10 \, \, cm = \frac{10}{100} \, \, m = 0.1 \, \, m \\ \\ \omega = \frac{\pi}{1800} \, \, rad/sec$


We can calculate linear velocity as follows:

$v = r\omega \\ \\ \implies v = 0.1 \times \frac{\pi}{1800} \\ \\ \implies v = \frac{\pi}{18000} \\ \\ \\ \implies \boxed{v \approx 1.745 \times 10^{-4} \, \, m/s}$


Thus, The Speed of the tip of the minute hand of the clock is $\bold{1.745 \times 10^{-4} \, \, m/s}$