Name: flywheel motion about a fixed axis
Uploaded: 2024-03-07T13:22:25.000Z
Duration: 1 min 18 s
Channel: JoVE

Imagine a flywheel having a non-uniform mass, rotating around a fixed axis. As the flywheel spins, its center of mass moves in a circular path.
The acceleration of the center of mass is described by its tangential and normal components.
The tangential component of acceleration depends on the direction of the angular acceleration of the flywheel. In contrast, the normal component of acceleration is always along the radius and towards the point O.
The moment exerted on the flywheel&#39;s center of mass is determined by the product of its moment of inertia of the center of mass and its angular acceleration.
The moment equation can be written in terms of the moment about point O to eliminate any unknown force acting on the body.
Here, the moment due to the normal component of the acceleration is not considered as it passes through point O.
Using the parallel axis theorem, the moment equation can be expressed in terms of the moment of inertia about point O.

equation of motion: rotation about a fixed axis

Equation of Motion: Rotation About a Fixed Axis

Consider a flywheel, having an uneven mass distribution, rotating steadily around a fixed axis. As this rotation occurs, the center of mass of the flywheel traces a circular path. Understanding the acceleration of this center of mass requires observing both its tangential and normal components.
The tangential component is dependent on the direction of the angular acceleration of the flywheel. The tangential component of the acceleration propels the flywheel along its path. On the other hand, the normal component is always directed along the radius towards point O. Point O lies on the axis of rotation along which the flywheel spins.
A crucial aspect of this scenario is the moment applied to the flywheel&#39;s center of mass. This is calculated by multiplying the moment of inertia of the center of mass by its angular acceleration. The equation for this moment can be articulated in terms of the moment about point O, which effectively eliminates any unknown forces acting on the body. Interestingly, the moment resulting from the normal component of acceleration is not taken into account in these calculations. The reason for this exclusion is that the normal component of the acceleration passes through point O and is parallel to the radial vector, resulting in no moment.
To further refine this understanding, one could employ the parallel axis theorem. This allows the moment equation to be expressed in terms of the moment of inertia about point O, providing a more detailed view of the flywheel&#39;s motion.

Imagine a flywheel having a non-uniform mass, rotating around a fixed axis. As the flywheel spins, its center of mass moves in a circular path.
The ...

equation-of-motion-rotation-about-a-fixed-axis

Education

JoVE Core

Mechanical Engineering

Unit 1

Planar Kinematics of a Rigid Body

KEY TERMS AND CONCEPTS

flywheel motion about a fixed axis

Flywheel motion about a fixed axis depends on how its mass is spread out and how it accelerates. In this case, the flywheel has an uneven mass distribution and rotates steadily around a fixed axis. As it spins, its center of mass follows a circular path.

The acceleration of the center of mass has two parts. The tangential component points along the path and depends on the direction of the flywheel’s angular acceleration. It helps move the flywheel along its circular path. The normal component points along the radius toward point O on the axis of rotation.

The moment on the flywheel’s center of mass is found by multiplying its moment of inertia by its angular acceleration. That equation can also be written using the moment about point O. This form removes unknown forces acting on the body and gives a cleaner equation of motion.

The normal component of acceleration does not add a moment in this setup. It passes through point O and is parallel to the radial vector, so its moment is zero. The parallel axis theorem can also be used to rewrite the moment equation with the moment of inertia about point O.

Flywheel Motion About 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...

rotational motion about a fixed axis

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...

kinematic equations for rotation

Rotation Kinematics: Velocity and Acceleration

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...

absolute motion analysis- general plane motion

absolute-motion-analysis-general-plane-motion

Drone Flight and General Plane Motion

Drone flight shows general plane motion, which combines translation and rotation. A drone lifts off when its spinning propellers create an upward force that balances gravity. This first movement is straight-line translational motion. During this stage, every point on the drone moves the same distance in the same direction. Once the drone is airborne, its motion becomes more complex. A point on the drone, such as point P, keeps moving while the drone flies. Point P follows a curved path instead...

relative motion analysis - velocity

Slider-Crank Velocity of Point B

A slider-crank mechanism converts rotational motion from a crank into linear motion of a slider, or the reverse. It has three main parts: the crank, the connecting rod, and the slider. When an external force acts on the system, the crank begins to rotate and drives the motion of the connecting rod. The connecting rod moves with general plane motion. In this motion, point A on the rod and point B on the crank both have translational motion. Point B also has rotational motion relative to point...

instantaneous center of zero velocity

Rolling Wheel Motion and the Instant Center

General plane motion can be seen in a rolling wheel. The wheel rotates and translates at the same time. To study this motion, the velocity of one point can be written as the vector sum of the velocity of another point and the relative velocity between them. A useful simplification is to choose a point that has zero velocity at a given instant. This point is called the instantaneous center of zero velocity, or IC. The IC lies on an axis perpendicular to the plane of motion. Where that axis...

relative motion analysis - acceleration

Slider-Crank Motion and Point B Acceleration

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...

relative motion analysis using rotating axes

relative-motion-analysis-using-rotating-axes

Velocity of Point B in a Rotating Frame

A rotating frame of reference helps describe the motion of point B on a moving member AB. The member has linear motion, and point B also rotates around point A. To track that motion, position vectors for A and B are first written in a fixed reference frame. A second frame, x'y', is then used to show the position of point B relative to point A. This frame both translates and rotates with the system. That makes it useful for analyzing the relative position more clearly. The velocity of point B...

relative motion analysis using rotating axes - acceleration

relative-motion-analysis-using-rotating-axes-acceleration

Acceleration of Point B in Rotating Axes

Acceleration of point B is found by analyzing a member AB that moves linearly and also rotates about point A. The motion is described with position vectors for points A and B in a fixed reference frame. This setup helps separate the motion of the point from the motion of the rotating frame. The absolute velocity of point B is written as the velocity of point A plus the relative velocity of point B in the rotating frame. It also includes the effect of angular velocity in that rotating frame. To...

relative motion analysis using rotating axes-problem solving

relative-motion-analysis-using-rotating-axes-problem-solving

Crane Boom Motion on Rotating Axes

Crane boom motion on rotating axes combines rotation and extension in one kinematics problem. A telescopic boom rotates while it also extends outward. Relative motion analysis helps find the velocity and acceleration of the moving end of the boom. In the setup, the boom rotates with an angular velocity of 0.04 rad/s and an angular acceleration of 0.02 rad/s². It also extends linearly at a constant speed of 5 m/s. The extension is measured at point D with respect to the fixed point C at the...

Flywheel motion about a fixed axis depends on how its mass is spread out and how it accelerates. In this case, the flywheel has an uneven mass distribution and rotates steadily around a fixed axis. As it spins, its center of mass follows a circular path. The acceleration of the center of mass has two parts. The tangential component points along the path and depends on the direction of the flywheel’s angular acceleration. It helps move the flywheel along its circular path. The normal component...

equation of motion: general plane motion

Rigid Body Motion: Forces and Moments

Rigid body motion in a general plane is driven by external forces and couple moments. The body moves and turns at the same time. Newton’s second law describes the translational motion of the center of mass along each axis. The center of mass also rotates because of the applied couple moments. That rotation is described by angular acceleration and moment of inertia. These two quantities connect the turning effect to how hard the body is to rotate. The same motion equations can be written for...

equation of motion: general plane motion - problem solving

equation-of-motion-general-plane-motion-problem-solving

Lawn Roller Angular Acceleration with Friction

A lawn roller’s angular acceleration can be found by using rolling motion and friction. The roller in this problem has a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied at an angle of 60 degrees from the horizontal. The setup also includes friction between the roller and the ground. The static friction coefficient is 0.15, and the kinetic friction coefficient is 0.1. The motion is treated as rolling without slipping, so the point of...

key terms and concepts

Learn how a flywheel’s center of mass moves in a circle, how tangential and normal acceleration differ, and how the moment equation is written about point O.

Flywheel Motion About 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.

mechanical engineering

Flywheel Motion About a Fixed Axis

Description

Transcript

Tags