Which one of the following is greater?(a) The angular velocity of the

1.	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?
Answer» 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 ∴ω_h \(=\frac{2\pi}{12}=\frac{\pi}{6}\) …(ii) T for each is 24 ℎ ∴ ω_e\(=\frac{2\pi}{24}=\frac{\pi}{12}\) 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 \(\omega_h>\omega_e\)

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?

Answer»

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

∴ω_h \(=\frac{2\pi}{12}=\frac{\pi}{6}\) …(ii)

T for each is 24 ℎ

∴ ω_e\(=\frac{2\pi}{24}=\frac{\pi}{12}\) 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 \(\omega_h>\omega_e\)