# Kinematics

In physics,**kinematics**is the branch of mechanics concerned with the motions of objects without being concerned with the forcess that cause the motion. In this latter respect it differs from dynamics, which is concerned with the forces that affect motion.

Because of its relative simplicity, kinematics is usually taught before dynamics or the concept of a force is introduced. The equations of motion are generally taught at secondary school level.

Table of contents |

2 Kinematic Constraints |

## Fundamental Equations

### Relative Motion

This is a simple equation from vector math that restates vector addition: motion of A relative to O is equal to the motion of B relative to O plus the motion of A relative to B:

### Rotating Frame

One fundamental equation in kinematics is the equation for the derivative of a vector described in a rotating frame of reference. As a sentence, it is: the time derivative of a vector in a fixed frame is equal to the derivative of the vector relative to the rotating frame plus the cross product of the angular velocity of the frame with the vector. In equation form that is:

where r(t) is a vector; X,Y,Z is the fixed frame; x,y,z is the rotating frame; and ω is the rate of rotation of the frame.

## Kinematic Constraints

### Rolling Without Slipping

An object that rolls against a surface without slipping obeys the condition that the velocity of its center of mass is equal to the cross product of its angular velocity with a vector from the point of contact to the center of mass, or:

For the case of an object that does not tip or turn, this reduces to v = R ω .

### Gears (no slip)

where r is a radius and ω is an angular velocity.

### Inextensible Cord

See example: point mass, rigid body.