# Kinematics of particles

**Part of the Dynamics course offered by the Division of Applied Mechanics, School of Engineering and the Engineering and Technology Portal**

## Lecture

edit### Equations of Motion

edit**Rectilinear Motion**

The motion of any particle is most easily described by using the the equations of Rectilinear Motion. Where represents distance or displacement, represents velocity and represents acceleration, it may be remembered from Physics that:

and

**Curvilinear Motion**

The motion of any particle along a curved path is most easily described by using the the equations of Curvilinear Motion. Where represents the position of a particle in cartesian or polar coordinates and is the displacement of said particle, the scalar quantity represents the distance of the displacement and is the *instantaneous velocity* of the particle:

```
```

### 3D Motion

editMotion in three dimensions may be described by the following equations:

**Rectangular Coordinates (Cartesian)** - (x,y,z)

**Cylindrical Coordinates** - (r, , z)

Also see Polar Coordinates (r, )

**Spherical Coordinates**
- (R, , )

### Mass Moment of Inertia

editMass Moment of Inertia is the resistance of an object to attempts to accelerate its rotation about an axis.

, , (4)

If the axis of rotation passes through the center of gravity of the rotating object, the calculated is called the Centroidal Mass Moment of Inertia. (See also the List of moments of inertia on Wikipedia)

### Additive Motion & Relative Motion

editFor a system of two vectors oriented in different directions, the relationsip between the two may be establshed through vector addition. For vectors and , the relative motion of from the frame of reference of is:

```
```

The calculation of relative motion is completed similarly for acceleration.

## Assignments

edit**Activities:**

- Create an activity

**Readings:**

- Peruse the appropriate sections of b:Mechanics

**Study guide:**

- Wikipedia article:Cartesian coordinates
- Wikipedia article:Polar coordinates
- Wikipedia article:Cylindrical coordinates
- Wikipedia article:Spherical coordinates
- Wikipedia article:Displacement
- Wikipedia article:Distance
- Wikipedia article:Velocity
- Wikipedia article:Speed
- Wikipedia article:Acceleration