Angular motion is the motion of an object around a fixed axis point, such as a swinging pendulum or an orbiting planet. By convention, measurements of angular motion are considered positive when the motion is counter-clockwise and negative when the motion is clockwise.
Angular displacement () is the change () in angle in radians () of the arc length () traveled by an object along a circular path. The angular displacement of an arc length equal to the radius () of a circle is, by definition, . Angular displacement can therefore be calculated as , though the is often omitted for brevity.
Angular displacement is the basis for angular motion because it allows all points on a rotating line to be measured, rather than just a single point by solving for the missing variable in the angular displacement calculation.
Angular velocity () is the change in angular displacement over the change in time (), or (again, the is often omitted). Essentially, "radians per second".
Angular velocity can be converted to speed (note that speed is not the same as velocity) by substituting arc length for angular displacement. Given and , therefore which equals and is distance over time, which is speed.
Angular acceleration () is the change in angular velocity over time, or . Essentially, "radians per second per second" or "radians per second squared".
Angular acceleration can be converted to tangential acceleration (), which is acceleration which doesn't account for the change in direction in circular motion, by substituting arc length for angular displacement. Given and , therefore , which is the change in angular velocity over time.
|Angular acceleration||Tangential acceleration||or|
Resources to Lean about Angular Motion
Deeper Knowledge on Angular Motion
Learn about gears and cogs
Learn about torque: Force that causes an object to rotate around an axis.
Broader Topics Related to Angular Motion
The angle which subtends an arc equal to the length of the radius of a circle
The fundamental nature and properties of matter, energy, and motion