Kinematics

Template:Infobox unit Template:Classical mechanics Angular acceleration is the rate of change of angular velocity. In SI units, it is measured in radians per second squared (rad/sShowcasing you the finest up and coming new condo launches in Singapore where you can search and discover the perfect house. Now we have new condo that may even satisfy the discerning few, it doesn't matter what's your necessities or your lifestyle needs. You'll certain to search out the dream apartment right here.

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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

${\alpha }={\frac {a_{T}}{r}}$ ,

where ${\omega }$ is the angular velocity, $a_{T}$ is the linear tangential acceleration, and $r$, (usually defined as the radius of the circular path of which a point moving along), is the distance from the origin of the coordinate system that defines $\theta$ and $\omega$ to the point of interest.

Equations of motion

For two-dimensional rotational motion (constant ${\hat {L}}$), Newton's second law can be adapted to describe the relation between torque and angular acceleration:

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

where ${\tau }$ 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, ${\tau }$, 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

• Angular momentum
• Angular speed
• Angular velocity
• Rotation
• Spin

References

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