Rotational Motion

Basic Definitions


Angular Motion

Angular motion, or rotational motion, is the movement of an object which is rotating around an axis.

Angular Displacement

Angular displacement ( θ ) is the angle through which the object rotates, measured in radians ( rad ).


360=2π radians.

Angular Velocity

Angular velocity ( ω ) is the rate of change of angular displacement, measured in radians per second ( rad s1 ).



Angular Acceleration

Angular acceleration ( α ) is the rate of change of angular velocity, measured in radians per second squared ( rad s2 ).

Alpha, not A!

Don't confuse α with a (linear acceleration)! They look similar, but they are the Greek letter alpha and the letter A respectively.



Linear Velocity

Linear velocity or tangential velocity ( v ) is the instantaneous linear velocity of a rotating object - it is the velocity of an object revolving around an axis if the tether breaks.

Linear Acceleration

Linear acceleration or tangential acceleration ( at ), like tangential velocity, is the instantaneous linear acceleration of a rotating object - it's the change in tangential velocity.



Radial Acceleration

Radial acceleration ( ar ) is the acceleration towards the centre of a rotating system, caused by centripetal force.



Variable Key

  • ar is the radial acceleration, in metres per second squared.
  • r is the radius of the rotating system, in metres.
  • ω is the angular velocity, in radians per second.
  • v is the linear velocity, in metres per second.

Equations of Motion

The equations of motion can be applied to angular motion as well as linear motion, as long as all tangential/linear quantities are substituted for their angular counterparts.

Quantity Linear Angular
Displacement s θ
Initial Velocity u ω0
Current Velocity v ω
Acceleration a α
Time (doesn't change!) t t

You can convert between linear and angular motion by multiplying or dividing the radius as a factor. To think about this intuitively, this is because c=2πr, and if the circumference is directly proportional to the radius, then velocity, acceleration, etc. must be directly proportional to the radius as well.