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Angular acceleration

 

 
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Angular acceleration
 
 
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Angular acceleration is the rate of change of angular velocityAngular velocity

In physics angular velocity is the speed at which something rotates together with the direction it rotates in....
 over timeTime

Two distinct views exist on the meaning of time....
. In SISi

Si, si, or SI may stand for:...
 units, it is measured in radianFacts About Radian

The radian is a unit of plane angle....
s per secondSecond

The second is the name of a unit of time, and today refers to the International System of Units base unit of time....
 squared (rad/s2), and is usually denoted by the Greek letter alphaAlpha (letter)

Alpha is the first letter of the Greek alphabet....
 .

Mathematical definition

The angular acceleration can be defined as either:

, or

,

where is the angular velocity, is the linear tangential accelerationAcceleration

In physics or physical science, acceleration is defined as the rate of change of velocity....
, and r is the radius of curvatureRadius of curvature

The distance from the center of a sphere or ellipsoid to its surface is its radius....
.

Equations of motion

For rotational motionRotation

Rotation is the movement of an object in a circular motion....
, can be adapted to describe the relation between torqueTorque

In physics, torque can informally be thought of as "rotational force"....
 and angular acceleration:

,
where is the total torque exerted on the body, and is the mass moment of inertiaFacts About Moment of inertia

Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, quantifies the rotationa...
 of the body.

Constant acceleration

For all constant values of the torque, , 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, constant value for the angular acceleration:

.

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 constant value. This differential equationDifferential equation

In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables....
 is known as the equation of motion of the system and can completely describe the motion of the object.

See also

  • Angular momentumAngular momentum

    In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the...
  • Angular speed
  • Angular velocityAngular velocity

    In physics angular velocity is the speed at which something rotates together with the direction it rotates in....
  • RotationRotation

    Rotation is the movement of an object in a circular motion....
  • SpinSpin (physics)

    In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the mo...


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