Question

The length of the second's hand of a clock is 10 cm. calculate its angular and linear velocity.
(Ans: Angular : 0.1047 rad/s, linear = 1.05 x 10 ^-2 m/s)

Answer 1

Given :

The length of the second's hand of a clock is 10cm.

To Find :

Angular and linear velocity of the second's hand.

Solution :

❖ Angular velocity of rotating body is given by

$\dag\:\underline{\boxed{\bf{\red{\omega=\dfrac{2\pi}{T}}}}}$

Where T denotes time period of revolution

We know that second's hand complete one revolution in 60 seconds.

$\sf:\implies\:\omega=\dfrac{2\pi}{60}$

$\sf:\implies\:\omega=\dfrac{3.14}{30}$

$\bf:\implies\:\omega=0.1047\:rad/s$

❖ Relation between angular velocity and linear velocity is given by

$\dag\:\underline{\boxed{\bf{\blue{v=r\:\omega}}}}$

Where r denotes radius

• r = 10cm = 0.1m

$\sf:\implies\:v=0.1\times0.1047$

$\bf:\implies\:v=1.05\times10^{-2}\:m/s$

Answer 2

Given :

The length of the second's hand of a clock is 10cm.

To Find :

Angular and linear velocity of the second's hand.

Solution :

❖ Angular velocity of rotating body is given by

$\dag\:\underline{\boxed{\bf{\red{\omega=\dfrac{2\pi}{T}}}}}$

Where T denotes time period of revolution

We know that second's hand complete one revolution in 60 seconds.

$\sf:\implies\:\omega=\dfrac{2\pi}{60}$

$\sf:\implies\:\omega=\dfrac{3.14}{30}$

$\bf:\implies\:\omega=0.1047\:rad/s$

❖ Relation between angular velocity and linear velocity is given by

$\dag\:\underline{\boxed{\bf{\blue{v=r\:\omega}}}}$

Where r denotes radius

r = 10cm = 0.1m

$\sf:\implies\:v=0.1\times0.1047$

$\bf:\implies\:v=1.05\times10^{-2}\:m/s$