Question

The second hand of a clock is 2.0 cm long .calculate the speed of the tip of the hand, the velocity at 0 seconds and at 15 seconds, the change in velocity from 0.0 to 15 seconds, and average acceleration.

Answer 1

We know second's hand complete one rotation in 60 sec

So we can write

${Angularvelocity}_{sec}=\frac{2\pi }{60}$ rad/s

We know,

$v=Angularvelocity\times r=\frac{2\pi }{60}\times 2=\frac{\pi }{15}$ cm/s

After 15 sec the position of the second hand will be as shown in the figure

So, $\Delta \overrightarrow{v}=\overrightarrow{-vi}-\overrightarrow{vj}=-v(\overrightarrow{i}+\overrightarrow{j})$

Or we can write

$\left|\overrightarrow{\Delta v}\right|=v\sqrt{2}=\frac{\pi }{15}\sqrt{2}$ cm/s

Now,

Average acceleration = $a=\frac{\Delta v}{t}=\frac{\frac{\pi }{15}\sqrt{2}}{15}=\frac{\pi }{225}\sqrt{2}$ cm/$s^2$