If you are an engineering student or an engineer, you probably know what it means for something to rotate.
But have you ever thought about how things move around an axis? This invisible line is called the axis of rotation.
It is a basic idea in engineering that helps you understand how things like gears and turbines move.
By understanding what the axis of rotation means, you can learn more about how things move when they rotate and gain a better understanding of how complicated the machines I use every day are.
In this article, I will talk about the basics of the axis of rotation and how important it is in engineering.
This will help you understand rotational motion in a whole new way.
Introduction to Axis of Rotation
A straight line passes through the points of a rotating, rigid body that remain stationary while the other points of the body move in circles about the axis.
A key idea in engineering, physics, and mechanics is the axis of rotation.
It is a made-up straight line that goes through a three-dimensional object and around which the object can turn or spin.
In other words, it is the line that a rigid body revolves around.
An inertial frame of reference shows that the axis of rotation can be fixed and does not move or change direction.
When every part of a body moves in a circle around a single line, called the axis of rotation, this is called pure rotational motion.
The fixed-axis hypothesis says that an axis can not change its position, so it can not explain things like wobbling or precession.
Internal Axis of Rotation
Objects in 3D space can have more than one axis of rotation inside them.
But it is not possible for an object to turn around two of these axes at the same time.
If an object's new axis of rotation is perpendicular to its original axis, it can not spin in opposite directions on both axes at the same time.
It will find a point where the two are balanced, and along that line, it will make a third axis of rotation.
Axis of Rotation in Human Anatomy
In anatomy, the axis of rotation is a made-up line that goes through the point where a joint turns or pivots.
For example, the axis of rotation for bending and straightening the arm goes through the elbow joint.
In human anatomy, there are three axes.
- The Anteroposterior Axis (Sagittal Axis) goes from front to back and from top to bottom of the body.
- Longitudinal Axis (Vertical Axis): It goes from top to bottom and from front to back through the body.
- Mediolateral Axis (Transverse Axis): It goes from left to right and from back to front of the body.
Orientation of a Rigid Body
The way a rigid body is oriented is determined by the way its own axes point.
This orientation is set by the rolling constraint and the instantaneous axis of rotation.
But this idea does not have much to do with the axis of rotation.
Tip: Turn on the caption button if you need it. Choose “automatic translation” in the settings button, if you are not familiar with the English language. You may need to click on the language of the video first before your favorite language becomes available for translation.
Axis of Rotation and Motion
Rotational motion is when a rigid body moves around an axis that does not move.
Rotational motion can be seen in the way the earth spins around its own axis and in the way wheels, gears, and motors move.
Engineers must think about rotational inertia when making things that spin, because it affects how well engines work and how propellers are made.
The variables and equations of rotational kinematics are used to solve real-world problems involving torque and lever arms.
You can solve examples of rotational motion by using the five rotational kinematic equations.
Also, rotational dynamics looks at the movement of an object and the forces that make it move.
The Kinematics and Dynamics of Fixed Axis Rotation
Rotation around a fixed axis is easier to figure out mathematically than free rotation of a rigid body because an axis can not change its position and it can not explain things like wobbling or precession.
Kinematics and dynamics of a rigid body rotating around a fixed axis are exactly the same as those of a rigid body moving in a single fixed direction.
This is not true for a rigid body that is free to rotate in any direction.
The expressions for the object's kinetic energy and the forces on its parts are also easier to write when the object rotates around a fixed axis instead of freely.
Rotational Inertia and Changing Rotational Velocity
When an object moves farther away from the axis of rotation, it gets harder and harder to change the system's speed of rotation.
This is because rotational inertia increases as mass moves away from the axis.
Rotational inertia is affected by both mass and the distance from the mass's center to the axis.
When something is pulled or pushed away from its center, it is harder to change how fast it spins.
This makes sense, because if someone is trying to spin something by pulling on one end, they are basically trying to make one side move faster than another side.
If one side has more weight or is farther from where the person is pulling, it will take more force to get that side moving at the same speed as the rest.
Stability of Rotating Objects
Whether or not something is stable when it is spinning depends on the main axes it spins around.
If there are no torques from the outside, an object spinning around one axis will wobble around some of its main axes but not others.
Any movement that goes against these axes can quickly get bigger and lead to much more complicated movement.
For example, a spinning top wobbles, but when the center of gravity is in line with the axis of rotation, it stops moving.
When designing rotating systems, the stability of the object and its main axes must be taken into account to make sure they work well and safely.
Moment of Inertia and Axis of Rotation
The moment of inertia is a way to measure rotational inertia, which is the resistance to change in angular velocity around a fixed axis.
It shows how much mass is near the axis of rotation and how much mass is farther away.
The moment of inertia is affected less by masses that are close to the axis and more by masses that are farther away.
The integral form of the equation for rotational kinetic energy can be used to figure out the moment of inertia.
This is because the moment of inertia and the square of the angular velocity are directly related.
Calculating Moments of Inertia
The integral form of the equation for rotational kinetic energy can be used to figure out the moment of inertia.
With this equation, you can figure out the moment of inertia of rigid bodies with regular shapes, like cylinders and spheres.
Experiments can be used to find the moment of inertia of bodies with different shapes.
The physical meaning of the moment of inertia is that it shows how hard it is to change the way an object rotates around an axis.
Objects with more mass farther from their axis will have a higher moment of inertia and be harder to turn than objects with less mass farther from their axis.
Applications of Moment of Inertia
In engineering and physics, the moment of inertia is a very important concept.
It is used, for instance, in the design of motors, turbines, and other machines and tools with moving parts.
Engineers also use the moment of inertia to figure out how stable things are when they spin around an axis.
Also, the moment of inertia is used to figure out how much torque is needed to make an object move in a certain way.
Torque and Angular Momentum
Torque is a way to measure the force that can turn something around an axis.
The harder it is for an object to gain angular acceleration, the bigger its rotational inertia.
This is a property of a rotating system that depends on how the system's mass is distributed.
For a system that rotates, the idea of rotational equilibrium is the same as Newton's first law.
If something is not rotating, it will stay that way unless an outside force changes it.
In the same way, an object that is rotating at a constant angular speed will continue to rotate unless an outside force acts on it.
Moment of Inertia
The moment of inertia (I) is equal to the sum of the masses of all the elements times their distances from the axis of rotation times four.
It is a key parameter for figuring out how easy or hard it is to change how something rotates.
The total torque that outside forces put on a system is equal to I times its angular acceleration.
If the torques acting on a body are not balanced, which means that the total torque is not zero, the body will rotate faster.
Newton's second law about rotations tells us how this works.
Conservation of Angular Momentum
When there are no torques from the outside, a system's total angular momentum stays the same.
This means that if there is no net external torque around a point in a fixed inertial reference frame, then the angular momentum of a system of particles around that point in space will stay the same.
The rotational versions of linear momentum and force are torque and angular momentum.
|The axis of rotation is used to control how robot joints and arms move. Engineers can program robots to do complicated tasks precisely and accurately by controlling the axis of rotation. For example, the axis of rotation is used to control how a robot arm moves as it welds car parts on an assembly line.
|Turbines, compressors, and other turbomachinery use the axis of rotation to transfer energy between parts that are moving and parts that aren't. Engineers must carefully plan the shape and location of the axis of rotation to make sure that the machine works as well and as efficiently as possible.
|The axis of rotation is a key part of how they are built and how stable they are. For a plane to be stable and easy to control, its center of gravity must be in line with its axis of rotation. Engineers use the axis of rotation to figure out the moments of inertia and design the aircraft's control systems.
|Structures like bridges, buildings, and dams are made with the axis of rotation in mind. Engineers have to make sure that the axis of rotation is in line with the load-bearing parts to make sure that the structure is stable and strong.
|The study of electricity
|Motors and generators are made with the axis of rotation in mind. In an electric motor or generator, the rotor spins around the axis of rotation to make electricity. Engineers must design the axis of rotation so that there is as little friction as possible and the most work is done.
In conclusion, the axis of rotation is a very important engineering concept that can tell us a lot about how things move when they are spinning.
By knowing the axis of rotation, you can analyze and design machines with more precision and accuracy, leading to designs that work better and are more efficient.
But besides being useful, the axis of rotation is also a reminder of how beautiful and complicated nature is.
The axis of rotation is at the center of all rotational motion, from the graceful spin of a top to the powerful motion of a turbine.
It connects us to the world around us in ways we may not even be aware of.
So, the next time you see something spinning, think about the invisible axis around which it spins and think about how amazing and complicated the forces that shape our world are.