Question

What is the angular speed of the second hand of a clock ? If the second hand is 10cm long, then find the linear speed of its tip .( in rad/s & m/s ).
A) 0.147, 0.0147
B) 1047, 0.01047
C) 0.1047, 1047
D) .0047, .01047

Answer 1

Angular speed of the second hand is given by:
(Angular speed) $\omega = \dfrac{{angular\,displacement}}{{time}}$
$\omega = \dfrac{\theta }{t}$ ($\theta$ is the angular displacement, t is the time.)
Using the above formula we will proceed to the problem.

Complete step by step answer:
Let’s define angular velocity or angular speed first and then we will discuss how much time the second hand of a clock completes one revolution.

Angular speed: angular velocity refers to how fast an object rotates or revolves relative to another point, that is how fast the angular position or orientation of an object changes with time. Angular speed is expressed as radians per second with the radian having a dimensionless value of unity.

Now we will do the calculation part:
When the second hand completes one revolution it is covered in 60 seconds and the angular distance covered is 3600 or in radians we can write as 2$\pi$ .
Therefore, angular speed is given as :
$\Rightarrow \omega = \dfrac{{2\pi }}{{60}}$ ( because speed=distance/time)
$\Rightarrow \omega = .1047rad/s$
Now, speed of linear tip v is given :
$\Rightarrow v = radius \times angular\,speed$
$\Rightarrow v = 10 \times .1047$ (radius of second hand is given as 10cm)
$\Rightarrow v = 1.047cm/s \\\ \Rightarrow v = \dfrac{{1.047}}{{100}}m/s \\\ \Rightarrow v = 0.01047m/s \\\$ (1m =100cm)

Thus, option 1 is correct.

Note:
Angular velocities are of two types: orbital angular velocity and spin angular velocity. Spin angular velocity refers to how fast a rigid body rotates with respect to its centre of rotation. Orbital velocity refers to how fast a point object revolves refers to how fast a point object revolves about a fixed point.