Pure Rotation

 

Rotation about a fixed axis

 

Pure rotation occurs when a body rotates about a fixed non-moving axis. The following figure illustrates fixed-axis rotation.

 

 

Motion characteristics

 

• Angular position: (θ) Angular position relative to an inertial coordinate axis. Similar to how θ was measured in polar coordinates.
• Angular velocity: (ω) How fast a body is rotating.
• Angular acceleration: (α) How fast a body's rotation rate is increasing or decreasing.

 

Angular kinematic relationships

 

• Angular velocity: The time rate of change of angular position. ω = dθ/dt
• Angular acceleration: The time rate of change of angular acceleration. α = dω/dt = d ²θ/dt ²
• Angular velocity / Angular acceleration: Combining the angular velocity and acceleration equations, we obtain α dθ = ω dω.

 

Angular motion parameter units

 

What are the units for angular position?

Check all that apply.

 

Radians
Radians per second
Radians per second squared
Degrees
Revolutions per minute

 

 

What are the units for angular velocity?

Check all that apply.

 

Radians
Radians per second
Radians per second squared
Degrees
Revolutions per minute

 

 

What are the units for angular acceleration?

Check all that apply.

 

Radians
Radians per second
Radians per second squared
Degrees
Revolutions per minute

 

 

Angular motion direction

 

If the rigid body, shown in the above figure, is rotating in the counterclockwise direction, what direction is its angular velocity?

 

i
-i
j
-j
k
-k