Name: angular motion around a fixed axis
Uploaded: 2024-03-07T13:22:24.000Z
Duration: 1 min 26 s
Channel: JoVE

When a rigid body rotates about a fixed axis, any given point within that body moves in a circular path around a specified line or point.
This type of rotation is defined by the angular position, represented by the angle &#952; which is measured from a fixed reference line to the rotating object.
The change from this angular position, quantified as a differential d&#952;, is termed angular displacement. The magnitude of this displacement can be measured in degrees, radians, or revolutions. Here, one revolution equal to 2&#960; radians.
The right-hand rule gives the direction of angular displacement, which is along the axis of rotation.
Angular velocity, denoted as &#969;, describes the rate of change of angular displacement. Angular velocity is measured in units of radians per second.
Furthermore, angular acceleration, denoted as &#945;, is the rate of change of angular velocity. It is measured in the units of radians per second squared.
Similar to angular displacement; both angular velocity and angular acceleration are vector quantities directed along the axis of rotation.

rotational motion about a fixed axis

Rotational Motion about a Fixed Axis

A rigid body&#39;s rotation around a fixed axis makes every point within it trace a circular path around a specific line or point. The term given to this type of spinning is defined by the angular position, symbolized by the angle &#952;. This angle is gauged from a static reference line to the revolving object. From this angular position, any variation is referred to as angular displacement, denoted by d&#952;. The extent of this displacement can be calculated in degrees, radians, or revolutions, where one revolution equals 2&#960; radians. This measurement helps in understanding the object&#39;s position in its rotational motion. The direction of angular displacement is determined by the right-hand rule, which means it aligns with the rotation axis.
Another aspect of rotational motion is angular velocity, symbolized by &#969;. It signifies the speed at which angular displacement changes and is quantified in radians per second. Angular velocity defines the rate at which the angular displacement changes over time and is measured in radians per second. Additionally, the concept of angular acceleration comes into play, symbolized by &#945;. Angular acceleration indicates how quickly or slowly the angular velocity changes over time. It is measured in the units of radians per second squared.
Like angular displacement, both angular velocity and angular acceleration are vector quantities, meaning they have both magnitude and direction. These vectors are oriented along the axis of rotation, indicating the direction of the rotation.
Understanding these concepts is fundamental to grasp the mechanics of rotational motion. They provide a comprehensive framework to comprehend how objects rotate and the forces that influence their movement.

When a rigid body rotates about a fixed axis, any given point within that body moves in a circular path around a specified line or point.
This type of ...

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Mechanical Engineering

Unit 1

Planar Kinematics of a Rigid Body

KEY TERMS AND CONCEPTS

angular motion around a fixed axis

Angular motion around a fixed axis describes how a rigid body spins around one line. As it rotates, each point in the body follows a circular path around that line or point. The motion is described using angular position, written as theta (θ), which is measured from a fixed reference line.

When angular position changes, the change is called angular displacement, written as dθ. Angular displacement can be measured in degrees, radians, or revolutions. One revolution equals 2π radians. This value helps show the object's new position in its rotational motion.

The direction of angular displacement follows the right-hand rule. This means the direction is aligned with the axis of rotation. Angular velocity, written as omega (ω), tells how fast angular displacement changes. It is measured in radians per second.

Angular acceleration, written as alpha (α), shows how quickly angular velocity changes over time. It is measured in radians per second squared. Angular displacement, angular velocity, and angular acceleration are all vector quantities. Their direction points along the axis of rotation, which helps describe the full motion of the spinning body.

Angular Motion Around a Fixed Axis

planar rigid-body motion

Types of Planar Rigid-Body Motion

Planar rigid-body motion describes the movement of a rigid body while its particles stay at a constant distance from a plane. This idea helps explain how objects move in physics and mechanical engineering. It also gives a clear way to study motion in space. One type of planar motion is rectilinear translation. In this motion, the body moves in a straight line. Any two points on the body follow parallel paths, like a subway train moving along its track or soldiers marching in step. Another...

Angular motion around a fixed axis describes how a rigid body spins around one line. As it rotates, each point in the body follows a circular path around that line or point. The motion is described using angular position, written as theta (θ), which is measured from a fixed reference line. When angular position changes, the change is called angular displacement, written as dθ. Angular displacement can be measured in degrees, radians, or revolutions. One revolution equals 2π radians. This value...

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Rotation kinematics describes the motion of a rigid body when it turns with constant angular acceleration. It follows the same basic ideas used in linear kinematics, but for circular motion instead of straight-line motion. For a point A on the rotating body, translational velocity comes from the time derivative of the displacement equation. This velocity is always tangent to the circular path of point A. It can also be written as the vector product of angular velocity and the position vector. <br...

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A slider-crank mechanism turns rotational motion from the crank into linear motion of the slider, and it can also work the other way around. It has three main parts: the crank, the connecting rod, and the slider. Because the angle between the crank and the connecting rod keeps changing, the motion is an example of general plane motion. To study the motion, a stationary reference system is placed at point O, and a translating frame is added at point A. The segment AB is then analyzed, with...

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Acceleration of Point B in Rotating Axes

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key terms and concepts

Learn how rigid bodies rotate about a fixed axis using angular position, displacement, velocity, and acceleration. Clear terms for grades 9–12.

Angular Motion Around a Fixed Axis | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Angular Motion Around a Fixed Axis

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