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Angular acceleration
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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 .
Mathematical definition The angular acceleration can be defined as either:
, or
,
where is the angular velocity, is the linear tangential acceleration, and r is the radius of curvature.
Equations of motion For rotational motion, can be adapted to describe the relation between torque and angular acceleration:
, where is the total torque exerted on the body, and is the mass moment of inertia of the body.
Constant accelerationFor 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 accelerationFor 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 equation is known as the equation of motion of the system and can completely describe the motion of the object.
See also
External links
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