Angular acceleration

Radians per second squared
Unit system	SI derived unit
Unit of	Angular acceleration
Symbol	rad/s² or rad⋅s⁻²

Classical mechanics
Part of a series of articles about
${\vec {F}}=m{\vec {a}}$ Second law of motion
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Angular acceleration is the rate of change of angular velocity. In three dimensions, it is a pseudovector. In SI units, it is measured in radians per second squared (rad/s²), and is usually denoted by the Greek letter alpha (α).^[1]

Mathematical definition

The angular acceleration vector is defined as:

{\boldsymbol {\alpha }}={\frac {d{\boldsymbol {\omega }}}{dt}}

where ${\boldsymbol {\omega }}$ (omega) is the angular velocity vector.

Equation of Motion

The angular acceleration of a point particle α can be connected to the applied torque τ by the following equation:

{I{\boldsymbol {\alpha }}}={\boldsymbol {\tau }}-2mr{\frac {d{r}}{dt}}{\boldsymbol {\omega }}

where m is the mass of the particle and I is its moment of inertia.

Above relationship indicates that, unlike the relationship between force and acceleration, the angular acceleration need not be directly proportional or even parallel to the torque. In fact, this is true whenever the moment of inertia of the particle changes with time.

References

↑ "Angular Velocity and Acceleration". Theory.uwinnipeg.ca. Retrieved 2015-04-13.

Classical mechanics SI units

Dimensions	1	L	L²	Dimensions	1	1	1
Linear/translational quantities				Angular/rotational quantities
T	time: $t$ s	absement: $A$ m s		T	time: $t$ s
1		distance: $d$ , position: $r$ , $s$ , $x$ , displacement m	area: $A$ m²	1		angle: $θ$ , angular displacement: $θ$ rad	solid angle: $Ω$ rad², sr
T⁻¹	frequency: $f$ s⁻¹, Hz	speed: $v$ , velocity: $v$ m s⁻¹	kinematic viscosity: $ν$ , specific angular momentum: $h$ m² s⁻¹	T⁻¹	frequency: $f$ s⁻¹, Hz	angular speed: $ω$ , angular velocity: $ω$ rad s⁻¹
T⁻²		acceleration: $a$ m s⁻²		T⁻²		angular acceleration: $α$ rad s⁻²
T⁻³		jerk: $j$ m s⁻³		T⁻³		angular jerk: $ζ$ rad s⁻³
M	mass: $m$ kg			ML²	moment of inertia: $I$ kg m²
MT⁻¹		momentum: $p$ , impulse: $J$ kg m s⁻¹, N s	action: $𝒮$ , actergy: $ℵ$ kg m² s⁻¹, J s	ML²T⁻¹		angular momentum: $L$ , angular impulse: $Δ L$ kg m² s⁻¹	action: $𝒮$ , actergy: $ℵ$ kg m² s⁻¹, J s
MT⁻²		force: $F$ , weight: $F g$ kg m s⁻², N	energy: $E$ , work: $W$ kg m² s⁻², J	ML²T⁻²		torque: $τ$ , moment: $M$ kg m² s⁻², N m	energy: $E$ , work: $W$ kg m² s⁻², J
MT⁻³		yank: $Y$ kg m s⁻³, N s⁻¹	power: $P$ kg m² s⁻³, W	ML²T⁻³		rotatum: $P$ kg m² s⁻³, N m s⁻¹	power: $P$ kg m²s⁻³, W

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Angular acceleration

Mathematical definition

Equation of Motion

See also

References