Angular acceleration

From Wikipedia, the free encyclopedia

Angular acceleration is the rate of change of angular velocity over time. In SI units, it is measured in radians per second squared (rad/s²), and is usually denoted by the Greek letter alpha (<math>{\alpha}\,</math>).

Contents 1 Mathematical definition 2 Equations of motion 2.1 Constant acceleration 2.2 Non-constant acceleration 3 See also

[edit] Mathematical definition

The angular acceleration can be defined as either:

<math>{\alpha} = \frac{d{\omega}}{dt} = \frac{d^2{\theta}}{dt^2}</math> , or

<math>{\alpha} = \frac{\mathbf{a}_{T}}{r}</math> ,

where <math>{\omega}</math> is the angular velocity, <math>\mathbf{a}_{T}</math> is the linear tangential acceleration, and r is the radius of curvature.

[edit] Equations of motion

For rotational motion, Newton's second law can be adapted to describe the relation between torque and angular acceleration:

<math>{\tau} = I\ {\alpha}</math> ,

where <math>{\tau}</math> is the total torque exerted on the body, and <math>I</math> is the mass moment of inertia of the body.

[edit] Constant acceleration

For all constant values of the torque, <math>{\tau}</math>, of an object, the angular acceleration will also be constant. For this special case of constant angular acceleration, the above equation will produce a definitive, singular value for the angular acceleration:

<math>{\alpha} = \frac{\tau}{I}</math> .

[edit] Non-constant acceleration

For any non-constant torque, the angular acceleration of an object will change with time. The equation becomes a differential equation instead of a singular value. This differential equation is known as the equation of motion of the system and can completely describe the motion of the object.

[edit] See also

• Angular momentum
• Angular speed
• Angular velocity
• Rotation
• Spinbs:Ugaono ubrzanje

cs:Úhlové zrychlení de:Winkelbeschleunigung es:Aceleración angular fr:Accélération angulaire ko:각가속도 pt:Aceleração angular hr:Kutno ubrzanje it:Accelerazione angolare ms:Pecutan sudut nl:Hoekversnelling no:Vinkelakselerasjon ru:Угловое ускорение sl:Kotni pospešek fi:Kulmakiihtyvyys tr:Açısal ivme uk:кутове прискорення zh:角加速度