聚焦环光学陷用于粒子轨道旋转

Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:

The Moon orbits around the Earth. In turn, the Earth (and other planets) orbit the Sun. The space directly above our atmosphere is filled with artificial satellites in orbit. One can examine the circular orbit, the simplest kind of orbit, to understand the relationship between the speed and the period of planets and satellites with respect to their positions and the bodies that they orbit.
Nicolaus Copernicus (1473-1543) first suggested that the Earth and all other planets orbit the Sun in...

A rigid body's rotation around a fixed axis makes every point within it trace a circular path around a specific line or point. The term given to this type of spinning is defined by the angular position, symbolized by the angle θ. This angle is gauged from a static reference line to the revolving object. From this angular position, any variation is referred to as angular displacement, denoted by dθ. The extent of this displacement can be calculated in degrees, radians, or...

Suppose a car moves on flat ground and turns to the left. The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. For this, a minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway. Let's now consider banked curves, where the slope of the road helps in negotiating the curve. The greater the angle of the curve, the faster one can take the curve. It is common for race tracks for...

An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed acceleration is called centripetal acceleration. This acceleration acts along the radius of the curved path (thus is also referred to as radial acceleration).
Any acceleration must be produced by some force. Therefore, any force or combination of forces can cause centripetal acceleration. A few examples include the tension in the rope on a...

In uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all circular motion occurs at a constant speed. A particle can travel in a circle and speed up or slow down, showing an acceleration in the direction of motion. In that case, the motion is called non-uniform circular motion, and an additional acceleration is introduced, which is in the direction tangential to the circle. 
For example, such...