angular acceleration

(noun)

The rate of change of angular velocity, often represented by α.

Related Terms

Examples of angular acceleration in the following topics:

  • Angular Acceleration, Alpha

    • Angular acceleration is the rate of change of angular velocity, expressed mathematically as $\alpha = \Delta \omega/\Delta t$ .
    • Angular acceleration is the rate of change of angular velocity.
    • Angular acceleration is defined as the rate of change of angular velocity.
    • In equation form, angular acceleration is expressed as follows:
    • The units of angular acceleration are (rad/s)/s, or rad/s2.

  • Relationship Between Torque and Angular Acceleration

    • Torque is equal to the moment of inertia times the angular acceleration.
    • Torque and angular acceleration are related by the following formula where is the objects moment of inertia and $\alpha$ is the angular acceleration .
    • If you replace torque with force and rotational inertia with mass and angular acceleration with linear acceleration, you get Newton's Second Law back out.
    • Torque, Angular Acceleration, and the Role of the Church in the French Revolution
    • Express the relationship between the torque and the angular acceleration in a form of equation

  • Constant Angular Acceleration

    • Constant angular acceleration describes the relationships among angular velocity, angle of rotation, and time.
    • Simply by using our intuition, we can begin to see the interrelatedness of rotational quantities like θ (angle of rotation), ω (angular velocity) and α (angular acceleration).
    • For example, if a motorcycle wheel has a large angular acceleration for a fairly long time, it ends up spinning rapidly and rotating through many revolutions.
    • Similarly, the kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time.
    • Relate angle of rotation, angular velocity, and angular acceleration to their equivalents in linear kinematics

  • Rotational Inertia

    • The first example implies that the farther the force is applied from the pivot, the greater the angular acceleration; another implication is that angular acceleration is inversely proportional to mass.
    • The greater the force, the greater the angular acceleration produced.
    • The more massive the wheel, the smaller the angular acceleration.
    • If you push on a spoke closer to the axle, the angular acceleration will be smaller.
    • Explain the relationship between the force, mass, radius, and angular acceleration

  • Torque

    • The torque in angular motion corresponds to force in translation.
    • It is the "cause" whose effect is either angular acceleration or angular deceleration of a particle in general motion .
    • Rotation is a special case of angular motion.
    • Torque can also be expressed in terms of the angular acceleration of the object.
    • The determination of torque's direction is relatively easier than that of angular velocity.

  • Rotational Angle and Angular Velocity

    • Although the angle itself is not a vector quantity, the angular velocity is a vector.
    • Angular acceleration gives the rate of change of angular velocity.
    • The angle, angular velocity, and angular acceleration are very useful in describing the rotational motion of an object.
    • The object is rotating with an angular velocity equal to $\frac{v}{r}$.
    • The direction of the angular velocity will be along the axis of rotation.

  • Angular vs. Linear Quantities

    • It has the same set of vector quantities associated with it, including angular velocity and angular momentum.
    • Thus, while the object moves in a circle at constant speed, it undergoes constant linear acceleration to keep it moving in a circle.
    • Just as there is an angular version of velocity, so too is there an angular version of acceleration.
    • When the object is going around a circle but its speed is changing, the object is undergoing angular acceleration.
    • Just like with linear acceleration, angular acceleration is a change in the angular velocity vector.

  • Relationship Between Linear and Rotational Quantitues

    • The description of motion could be sometimes easier with angular quantities such as angular velocity, rotational inertia, torque, etc.
    • The velocity (i.e. angular velocity) is indeed constant.
    • Similarly, we also get $a = \alpha r$ where $a$ stands for linear acceleration, while $\alpha$ refers to angular acceleration (In a more general case, the relationship between angular and linear quantities are given as $\bf{v = \omega \times r}, ~~ \bf{a = \alpha \times r + \omega \times v}$. )
    • With the relationship of the linear and angular speed/acceleration, we can derive the following four rotational kinematic equations for constant $a$ and $\alpha$:
    • For the description of the motion, angular quantities are the better choice.

  • Kinematics of UCM

    • Under uniform circular motion, angular and linear quantities have simple relations.
    • We define angular velocity $\omega$ as the rate of change of an angle.
    • Under uniform circular motion, the angular velocity is constant.
    • This acceleration, responsible for the uniform circular motion, is called centripetal acceleration.
    • For uniform circular motion, the acceleration is the centripetal acceleration: $a = a_c$.

  • Accretion Disks

    • The preceding section ignores an important aspect of accretion: the angular momentum of the accreta.
    • If the material starts with some net angular momentum it can only collapse so far before its angular velocity will be sufficient to halt further collapse.
    • First let's see why angular momentum can play a crucial role in accretion.
    • The initial specific angular momentum is $v b$.
    • If the material conserves angular momentum we can compare the centripetal acceleration with gravitational acceleration to give