Angular acceleration

Physical size
Surname	Angular acceleration
Formula symbol	${\displaystyle {\vec {\alpha }}}$
Derived from	Angular velocity
Size and unit system unit dimension SI rad · s −2 T −2

The angular acceleration ( symbol : α ) describes the change in the angular speed of a rotating object over time. It is a vector quantity (more precisely: a pseudo vector ). Mathematically speaking, it is the derivative of the angular velocity with respect to time . In many cases in which the direction of the axis of rotation does not change in the reference system, it is sufficient to use the scalar as the amount of the vector. ${\displaystyle {\vec {\omega }}}$

${\displaystyle {\alpha (t)}={\frac {\mathrm {d} \omega }{\mathrm {d} t}}={\frac {\mathrm {d^{2}} \varphi }{\mathrm {d} t^{2}}}}$ , or

${\displaystyle {\alpha }={\frac {{a}_{T}}{R}}}$ ,

The SI unit of angular acceleration is rad / s ² ( radians per second squared).

The angular acceleration must be differentiated from the tangential acceleration of a point, which is the derivation of the path velocity over time. ${\displaystyle {a}_{T}}$

For a rigid body with the moment of inertia, the relationship between the torque and the angular acceleration is : ${\displaystyle M}$ ${\displaystyle I}$

${\displaystyle I\cdot \alpha =M}$.

In vector form, the change in angular momentum is equal to the external moment ( Euler's equation ): ${\displaystyle {\vec {L}}}$

${\displaystyle {\dot {\vec {L}}}={\bar {I}}\cdot {\dot {\vec {\omega }}}={\vec {M}}}$.

Therefore, angular accelerations play in the art, among other things an important role in pulleys -Antrieben, shafts , electric motors , centrifuges (z. B. drum of the washing machine and dryer ) and wheels of vehicles . If the drive causes an angular acceleration that is too high, the maximum permissible torque can be exceeded and, for example, a drive belt can slip or a shaft can be damaged or destroyed.

In astronomy , the angular acceleration of a planet around its sun is related to the law of area (second Kepler law). As the planet approaches the central body, its angular velocity increases.

Individual evidence

1. ↑ Jürgen Dankert, Helga Dankert: Technical mechanics: statics, strength theory, kinematics / kinetics . 5th edition. Vieweg + Teubner, 2009, ISBN 978-3-8351-0177-7 , pp. 470 ( limited preview in Google Book search).