Question

​calculate the angular speed of he second hand of a clock. if the length of the second hand is 4cm , calculate the speed of the tip of the second hand ?

Answer 1

Step 1: Given that:

Length of second hand of the clock= $4cm$

Step 2: Calculation of angular speed of the second hand:

As the second hand of the clock completes its one round in $60sec$ .

Time period($T$)= $60sec$

The length of the second hand act as the radius of the circular path of the motion of second hand of the clock.

Thus,

Angular speed($\text{ω}$) = $\frac{2\pi }{T}$

$\text{ω}=\frac{2\pi }{60}$

$\text{ω}=\frac{\pi }{30}rad{s}^{-1}$

Step 3: Calculation of speed of second hand:

Speed = $Angularspeed\times Radius$

= $4\times \frac{\pi }{30}rad{s}^{-1}$

= 0.42cm/s

Thus,

Angular speed= $\frac{\pi }{30}rad{s}^{-1}$

speed= $0.42cm{s}^{-1}$