Rotational Motion
Beginner
rotational motion
Source: High school physics (Chinese)
Problem Sets:
Rigid body - 1111
Problem
Calculate the angular velocities of the Earth's daily rotation about its axis and its annual revolution about the Sun.
- What is the angular velocity of the Earth's rotation?
- What is the angular velocity of the Earth's revolution?
[Q1] $\omega_{rot} = 7.27 \times 10^{-5} \text{ rad/s}$ [Q2] $\omega_{rev} = 1.99 \times 10^{-7} \text{ rad/s}$
The angular velocity is defined as $\omega = 2\pi/T$, where $T$ is the period.
[Q1] For Earth's rotation, the period is $T_{rot} = 1 \text{ day} = 86400 \text{ s}$.
$$\omega_{rot} = \frac{2\pi}{T_{rot}} = \frac{2\pi \text{ rad}}{86400 \text{ s}}$$[Q2] For Earth's revolution, the period is $T_{rev} = 1 \text{ year} \approx 365.25 \text{ days} = 3.156 \times 10^7 \text{ s}$.
$$\omega_{rev} = \frac{2\pi}{T_{rev}} = \frac{2\pi \text{ rad}}{3.156 \times 10^7 \text{ s}}$$