Question 285: Work, Energy and Power & Circular Motion

Question

If $$\omega_1$$ is angular velocity of hour hand of clock and $$\omega_2$$ is angular velocity of the earth, then the ratio $$\omega_1$$ : $$\omega_2$$ is

Accepted Answer

To determine the ratio of the angular velocities of the hour hand of a clock ($$\omega_1$$) and the Earth ($$\omega_2$$), let's first understand the angular velocities involved:
The hour hand of a clock completes one full revolution in 12 hours. Therefore, the angular velocity $$\omega_1$$ can be calculated as follows:
$$ \omega_1 = \frac{2\pi 	ext{ radians}}{12 	ext{ hours}} = \frac{\pi}{6} 	ext{ radians per hour} $$
The Earth completes one full revolution (360 degrees or $$2\pi$$ radians) in about 24 hours. Hence, the angular velocity $$\omega_2$$ of the Earth is:
$$ \omega_2 = \frac{2\pi 	ext{ radians}}{24 	ext{ hours}} = \frac{\pi}{12} 	ext{ radians per hour} $$
Now, to find the ratio $$\omega_1$$ : $$\omega_2$$, we divide $$\omega_1$$ by $$\omega_2$$:
$$ \frac{\omega_1}{\omega_2} = \frac{\frac{\pi}{6}}{\frac{\pi}{12}} = \frac{\pi}{6} 	imes \frac{12}{\pi} = 2 $$
Thus, the ratio $$\omega_1$$ : $$\omega_2$$ is:
$$ 2 : 1 $$
So, the correct answer is:
Option D: 2 : 1

Answer

1 : 2

Answer

2 : 3

Answer

3 : 2

Answer

2 : 1

Work, Energy and Power & Circular Motion

If $\omega_1 is angular velocity of hour hand of clock and \omega_2 is angular velocity of the earth, then the ratio \omega_1 : \omega_2$ is

Choose the correct answer: