Question

The angular velocity of the revolution of a planet around the sun increases. Why?

Answer 1

Step 1. Angular velocity:

1. Angular velocity may be defined as the rate of change of the position angle of an object with respect to time,
2. Angular velocity is less common than linear velocity since it only concerns objects that are moving along a circular path.
3. For example, a roulette ball on a roulette wheel, a race car on a circular path, and a Ferris wheel are all examples of angular velocity.
4. The unit of angular velocity is radian per second.

Step 2. Mathematical expression for Angular velocity:

$\omega =\frac{\theta }{t}$ where $\omega$= angular velocity, $\theta$= position angle, and $t$ = time.

Step 3. Angular velocity increases, when a planet revolves around the sun:

1. According to the Law of Conservation of Angular Momentum, the total angular momentum of the system remains constant when the sum of external torques is zero.
2. Thus for a Sun planet system, the angular momentum is conserved.
3. As angular speed and distance from the sun are inversely related to each other.
4. Also, the angular velocity of the revolution of the planets around the sun increases and this can be explained using Kepler’s second law.
5. It is observed that as the planet gets closer to the sun, the planets move faster because the gravitational pull from the sun gets stronger.
6. Also, the moment of inertia about the axis decreases for all the planets.
7. Angular velocity increases to conserve angular momentum.
8. The moment of inertia of the earth about an axis measured through the sun keeps on changing due to changes in its distance from the sun

Hence, the angular velocity of the planets around the sun increases because the gravitational pull from the sun gets stronger.