- #1
Petr Mugver said:Rotations don't commute. In other words a rotation by w1 followed by a rotation by w2 is different than w2 followed by w1, and in any case is NOT w1 + w2.
Yes and no. Those two vectors ω1 and ω2 are not expressed in the same reference frames. One of them has to be transformed so that they can be added. Angular velocities are typically expressed in rotating frame coordinates. Three reasons:wzy75 said:Isn't the absolute angular velocity of the second frame (please see the figure) w1+w2?
Angular acceleration is the rate at which an object's angular velocity changes. It is a measure of how quickly an object's rotation is speeding up or slowing down.
Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula for angular acceleration is α = (ω2 - ω1) / Δt.
The units of angular acceleration are radians per second squared (rad/s2) or degrees per second squared (deg/s2).
Angular acceleration is a measure of how an object's rotation is changing, while linear acceleration is a measure of how an object's linear velocity is changing. Angular acceleration is measured in units of radians per second squared, while linear acceleration is measured in units of meters per second squared.
When two frames are rotating, the angular acceleration of an object in one frame will be different from the angular acceleration of the same object in the other frame. This is because the two frames have different angular velocities, which will result in different angular accelerations for the same object.