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 zaxis 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
