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angular acceleration

 
Dictionary: angular acceleration

n.
The rate of change of angular velocity with respect to time.


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The rate at which angular velocity changes with respect to time. Angular acceleration = (final angular velocity−initial angular velocity)/time.

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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 (α).[1]

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Mathematical definition

The angular acceleration can be defined as either:

{\alpha} = \frac{d{\omega}}{dt} = \frac{d^2{\theta}}{dt^2} , or
{\alpha} = \frac{\mathbf{a}_{T}}{r} ,

where ω is the angular velocity, \mathbf{a}_{T} is the linear tangential acceleration, and r is the radius of curvature.

Equations of motion

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

{\tau} = I\ {\alpha} ,

where τ is the total torque exerted on the body, and I is the mass moment of inertia of the body.

Constant acceleration

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:

{\alpha} = \frac{\tau}{I}.

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 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.

See also

References


Best of the Web: angular acceleration
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Some good "angular acceleration" pages on the web:


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Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.  Read more
Sports Science and Medicine. The Oxford Dictionary of Sports Science & Medicine. Copyright © Michael Kent 1998, 2006, 2007. All rights reserved.  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Angular acceleration" Read more