Question

Calculate the angular velocity and linear velocity of a tip of minute hand length 10cm.

Answer 1

Hints: There is a relation between angular velocity and linear velocity. Once we find angular velocity then by multiplying it by radius, linear velocity.

Formula Used: $\omega = \dfrac{{d\theta }}{{dt}}$, where $\omega =$ Angular velocity
$d\theta$ is the angular displacement covered in $dt$ time.
$V = \omega \times r$, here $V$ is the linear velocity and $r$ is the radius.

Complete step by step answer: In this question, for getting the angular velocity, we should know that if a minute hand completes one is 3600 seconds and one rotation covers $360^\circ$ equivalent to $2\pi$ radian (any circular distance must be expressed in radian).
Now, if we come to the formula of angular velocity, is angular displacement divided by change in time $dt$ .
So, we have considered that here angular displacement is $2\pi \left( {radian} \right)$ and time in which a minute hand completes its required distance is 3600 seconds.
$\omega = \dfrac{{2\pi \left( {rad} \right)}}{{3600\left( {\sec } \right)}} = 1.745 \times {10^{ - 3}}rad/\sec$
Now, if we want to find linear velocity, we only need to know radius.
Here, the length $\left( l \right)$ of minute hand represent radius $\left( r \right)$
$l = r = 10cm = 0.1m$
$V = \omega \times r = 1.745 \times {10^{ - 3}} \times 0.1$
$= 1.745 \times {10^{ - 4}}m/s$

Note: In these types of questions, we must keep one thing in our mind that the unit must be in meters and the unit of angular velocity must be in radian/second.