了解粗粒度模型中的动态. 三,第三部分. 旋转运动和转向-旋转合在粗粒动力学中的作用

In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
For instance, imagine a point A on a rigid body engaged in circular motion. The translational velocity of this particular point can be calculated by taking the time derivatives of the displacement equation, which essentially measures the...

Angular variables are introduced in rotational dynamics. Comparing the definitions of angular variables with the definitions of linear kinematic variables, it is seen that there is a mapping of the linear variables to the rotational ones. Linear displacement, velocity, and acceleration have their equivalents in rotational motion, which are angular displacement, angular velocity, and angular acceleration. Similar to the rotational variables, a mapping exists from Newton's second law of motion...

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...

Consider a flywheel, having an uneven mass distribution, rotating steadily around a fixed axis. As this rotation occurs, the center of mass of the flywheel traces a circular path. Understanding the acceleration of this center of mass requires observing both its tangential and normal components.
The tangential component is dependent on the direction of the angular acceleration of the flywheel. The tangential component of the acceleration propels the flywheel along its path. On the other hand,...

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...

The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...