Kinematics Totally Explained

Everything about Kinematics totally explained

Kinematics (Greek κινειν,kinein, to move) is a branch of dynamics which describes the motion of objects without the consideration of the masses or vectors that bring out the motion. In contrast, kinetics is concerned with the forces and interactions that produce or affect the motion. The simplest application of kinematics is to point particle motion (translational kinematics or linear kinematics). The description of rotation (rotational kinematics or angular kinematics) is more complicated. The state of a generic rigid body may be described by combining both translational and rotational kinematics (rigid-body kinematics). A more complicated case is the kinematics of a system of rigid bodies, possibly linked together by mechanical joints. The kinematic description of fluid flow is even more complicated, and not generally thought of in the context of kinematics.

Translational motion

Translational or curvilinear kinematics is the description of the motion in space of a point along a trajectory. This path can be linear, or curved as seen with projectile motion. There are three basic concepts that are required for understanding translational motion:

Displacement is the shortest distance between two points: the origin and the displaced point. The origin is (0,0) on a coordinate system that's defined by the observer. Because displacement has both magnitude (length) and direction, it's a vector whose initial point is the origin and terminal point is the displaced point.

Velocity is the rate of change in displacement with respect to time; that's the displacement of a point changes with time. Velocity is also a vector. For a constant velocity, every unit of time adds the length of the velocity vector (in the same direction) to the displacement of the moving point. Instantaneous velocity (the velocity at an instant of time) is defined as

vec v = frac

.

For the case of an object that doesn't tip or turn, this reduces to v = R ω.

Inextensible cord

This is the case where bodies are connected by some cord that remains in tension and can't change length. The constraint is that the sum of all components of the cord, however they're defined, is the total length, and the time derivative of this sum is zero.

Further Information

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