# Which one of the following is greater? (a) The angular velocity of the hour hand of a watch?

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Which one of the following is greater?

(a) The angular velocity of the hour hand of a watch?

(b) The angular velocity of the earth around it own axis. Why?

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The angular velocity of hour hand of a watch is greater than the angular velocity of earth around its own axis.

Explanation – We know that angular velocity (ω) of an object having time period (T) is given by ω = $\frac{2\pi}{v}$ …(i)

T for hour hand of a watch is 12 ℎ

ωh $=\frac{2\pi}{12}=\frac{\pi}{6}$ …(ii)

T for each is 24 ℎ

ωe   $=\frac{2\pi}{24}=\frac{\pi}{12}$ rad h-1

Equations (ii), (iii) gives,

$\frac{\omega_h}{\omega_e}=\frac{\frac{\pi}{6}}{\frac{\pi}{12}}=2$

or $\omega_h=2\omega_e$

or $\omega_h>\omega_e$