Angular acceleration is the rate of change of angular velocity over time. In SI units, it is measured in radians per second squared (rad/s^{2}), and is usually denoted by the Greek letter alpha (α).^{[1]}
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The angular acceleration can be defined as either:
where ω is the angular velocity, is the linear tangential acceleration, and r is the radius of curvature.
For rotational motion, Newton's second law can be adapted to describe the relation between torque and angular acceleration:
where τ is the total torque exerted on the body, and I is the mass moment of inertia of the body.
For all constant values of the torque, τ, 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:
For any nonconstant 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. It is also the best way to calculate the angular velocity.
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Angular acceleration is a vector whose magnitude is defined as the change in angular velocity in unit time.
It is in in SI unit.
Analogous to translational acceleration, , angular acceleration has the defining formula:
in which represents an instantaneous change in angular velocity,which takes place in , a short flitting time.
Equivalently, think about the limiting case:
The angular acceleration of an fixedaxisobject is proportional to the net torque applied.
in which is the Moment of Inertia of the object.
When an rotation has constant angular acceleration , the angle displacement covered in a given time is given by an equation that is strikingly similar to the equation for displacement under constant acceleration.
in which is the angular velocity at the beginning of the time period
in which case the angular velocity at the beginning is "zero"
in which is the angular velocity at the end of the time period
