angular motion

(noun)

The motion of a body about a fixed point or fixed axis (as of a planet or pendulum). It is equal to the angle passed over at the point or axis by a line drawn to the body.

Related Terms

Examples of angular motion in the following topics:

  • 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 description of circular motion is described better in terms of angular quantity than its linear counter part.
    • When we describe the uniform circular motion in terms of angular velocity, there is no contradiction.
    • This is the first advantage of describing uniform circular motion in terms of angular velocity.
    • For the description of the motion, angular quantities are the better choice.

  • 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 .
    • Similar to Newton's Second Law, angular motion also obeys Newton's First Law.
    • If no outside forces act on an object, an object in motion remains in motion and an object at rest remains at rest.
    • Torque, Angular Acceleration, and the Role of the Church in the French Revolution

  • Angular vs. Linear Quantities

    • The familiar linear vector quantities such as velocity and momentum have analogous angular quantities used to describe circular motion.
    • Linear motion is motion in a straight line.
    • Similarly, circular motion is motion in a circle.
    • However, we can define an angular momentum vector which is constant throughout this motion.
    • Constant angular velocity in a circle is known as uniform circular motion.

  • Kinematics of UCM

    • Uniform circular motion is a motion in a circular path at constant speed.
    • Under uniform circular motion, angular and linear quantities have simple relations.
    • We define angular velocity $\omega$ as the rate of change of an angle.
    • In symbols, this is $\omega = \frac{\Delta \theta}{\Delta t}$, where an angular rotation $\Delta\theta$ takes place in a time $\Delta t$.
    • Under uniform circular motion, the angular velocity is constant.

  • Angular Acceleration, Alpha

    • Angular acceleration is the rate of change of angular velocity.
    • Angular acceleration is defined as the rate of change of angular velocity.
    • An object undergoing circular motion experiences centripetal acceleration (as seen in the diagram below.)
    • Centripetal acceleration occurs as the direction of velocity changes; it is perpendicular to the circular motion.
    • In circular motion, acceleration can occur as the magnitude of the velocity changes: a is tangent to the motion.

  • Constant Angular Acceleration

    • Constant angular acceleration describes the relationships among angular velocity, angle of rotation, and time.
    • Kinematics is the description of motion.
    • Similarly, the kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time.
    • To determine this equation, we use the corresponding equation for linear motion:
    • This figure shows uniform circular motion and some of its defined quantities.

  • Rolling Without Slipping

    • The motion of rolling without slipping can be broken down into rotational and translational motion.
    • Rolling without slipping can be better understood by breaking it down into two different motions: 1) Motion of the center of mass, with linear velocity v (translational motion); and 2) rotational motion around its center, with angular velocity w.
    • If we imagine a wheel moving forward by rolling on a plane at speed v, it must also be rotating about its axis at an angular speed $\omega$ since it is rolling.
    • where $dx/dt$ is equal to the linear velocity $v$, and dθ/dt is equal to the angular velocity $\omega$.
    • Distinguish the two different motions in which rolling without slipping is broken down

  • Rotational Angle and Angular Velocity

    • When an object rotates about an axis, as with a tire on a car or a record on a turntable, the motion can be described in two ways.
    • 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.

  • Rotational Collisions

    • This fact is readily seen in linear motion.
    • What if an rotational component of motion is introduced?
    • For objects with a rotational component, there exists angular momentum.
    • Angular momentum is defined, mathematically, as L=Iω, or L=rxp.
    • An object that has a large angular velocity ω, such as a centrifuge, also has a rather large angular momentum.

  • Conservation of Angular Momentum

    • The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.
    • There appears to be a numerical quantity for measuring rotational motion such that the total amount of that quantity remains constant in a closed system.
    • The symbol for angular momentum is the letter L.
    • We can see this by considering Newton's 2nd law for rotational motion:
    • If the change in angular momentum ΔL is zero, then the angular momentum is constant; therefore,