Rotational Kinematics

SI units & Physics constants

Rotational kinematics investigates lows of motion of objects along circular path without any reference to forces that cause the motion to change

Here (all units see here):

 is initial time on time interval  in seconds

 is final time

 is original angular position at time  in radians

 is final angular position at time

 is angular displacement during time

 is original linear velocity vector at time tangent to trajectory

 is final linear velocity vector at time , tangent to trajectory

 is total linear acceleration vector, in plane of motion

 is normal component of total acceleration vector

 is tangential component of total acceleration vector

 is radius vector of trajectory, normal to trajectory

 is length of path during time

is angular velocity vector, normal to plane of motion

 is angular acceleration vector, normal to plane of motion

General formulas

Angular displacement

Average angular speed on time interval

Instantaneous angular speed at time

Original angular speed at time

Instantaneous angular velocity vector

where  is unit vector of z-axis shown in the above diagram

Instantaneous angular acceleration vector

Linear velocity vector is defined by vector product, where is perpendicual to

Magnitude of linear velocity

Magnitude of normal component of total linear acceleration

Magnitude of tangential component of total linear acceleration

Total linear acceleration vector is defined by vector sum

Magnitude of total linear acceleration

Angle between linear acceleration and linear velocity vectors

Relation between angular acceleration and angular velocity

Kinematic equation for rotation

Uniform rotation

Uniformly accelerated rotation

At  the rotation is accelerated

At  the rotation is decelerated