Question

The second's hand of a watch is 2 cm long. The speed of the tip of this hand is.?

Please answer with full statement and calculation.

Answer 1

v= wr where w stands for angular velocity and r for length of second's hand
w=2π/60
V=2π/60×0.02 m/s

Answer 2

The second hand’s tip speed is 0.21 cm/s

Given:

Length = 2 cm

To find:

Speed = ?

Solution:

$\text{Speed} =\frac{\text {Distance}}{\text {Time}}$

Distance = Circumference of the circle

$\text{ Circumference of the circle } = 2 \pi r$

Radius = r = length of the seconds hand

$\text{Distance} =2 \pi r$

$\text{Distance} =2 \times \frac{22}{7} \times 2$

$\Rightarrow \text { Distance }=12.57 \ \mathrm{cm}$

The time taken by the seconds hand to complete circumference is 60 seconds.

$\therefore \text { Speed }=\frac{12.57}{60}$

$\text { Speed } = 0.209$

Thus, the seconds hand’s speed is,

$\Rightarrow \text { Speed }=0.21 \ \mathrm{cm} / \mathrm{s}$