1 December 2023 The axis of rotation is an imaginary line around which an object can rotate. This concept is used in both mathematics and physics. In mathematics, the axis of rotation is a line that crosses a geometric object and that is used to calculate the amount of rotation that this object performs around it. The axis of rotation is important in three-dimensional geometry, since it allows to identify the angles and distances of an object in space.

In physics, the axis of rotation is used to describe the motion of rotating bodies. A body in rotation revolves around its axis, and the speed and direction of its rotation they can be measured using tools such as the gyroscope. In addition, the axis of rotation is also important in classical mechanics, where the movement of objects is studied in relation to their mass, speed, and force.

The axis of rotation is critical in the law Of Conservation Of Angular Momentum, which states that the amount of angular momentum of a rotating object remains constant as long as there are no external forces acting on it.

## Definition and concept of the axis of rotation

The axis of rotation is a limaginary line that crosses every body at the point where it rotates on itself. This line is also often called the axis of symmetry and is one of the main concepts in the study of physics and mechanics.

When an object or body rotates on its axis of rotation, it is said to be revolving around that point. The rotation can be both clockwise and counterclockwise, and the speed of rotation can vary depending on the force applied to the object. It is a fundamental concept in describing the motion of rigid bodies in space, and is used in various branches of physics, such as classical mechanics, quantum physics, and relativistic physics.

Regarding the shape of bodies, those that have a symmetrical shape are said to have an axis of rotation that passes through their center. For example, a sphere, a cylinder or a cube have a central axis of rotation, while other bodies with irregular shapes they will have more complex axes of rotation.

It should be noted that, in the real world, no object is perfectly symmetrical, so the axis of rotation will not always pass through the center of the object. In some cases it can move to the side or even be outside the body.

### What is the axis of rotation in physics?

It is a fundamental concept in physics and it is important to understand its definition to understand how moving objects behave. When an object rotates, it does so around an axis, which it can be an imaginary axis or a physical one. For example, a top spins around a physical axis through the center of the top, while the Earth spins around an imaginary axis through the north and south poles.

If the object is rotating uniformly, that is, at a constant speed, then the axis of rotation remains fixed in space and the object revolves around it. The axis of rotation is a line extending from the object’s center of mass outward.

In the case of a symmetric object, the axis of rotation may be visible, such as in a circle, but on asymmetric objects, the axis of rotation may be more difficult to visualize. For example, the axis of rotation of a human body it would be difficult to visualize because the body has many irregular shapes.

Furthermore, the axis of rotation is also important in understanding Newton’s laws of motion. Newton’s first law says that a object at rest will remain at rest or in uniform rectilinear motion unless acted upon by an external force.

However, when the object is rotating around an axis, this law applies slightly differently. Newton’s first law for a rotating object is that a rotating object will remain in that uniform motion unless a external force acting on it to alter its axis of rotation.

### What is the axis of rotation in mathematics?

In mathematics, rotation is an important tool for describing rotations in three-dimensional space. One of the most common examples of an object that revolves around an axis of rotation it’s a top When a top is thrown, physical forces cause it to spin around a central axis of rotation. This creates a continuous, stable circular motion as the top spins at high speed.

The axis of rotation is an imaginary line that lies in the center of a solid object and around which it rotates. For example, if someone rotates an office chair in the air, it moves around a vertical axis through the center of the seat. A solid of revolution is obtained by rotating a two-dimensional figure about an axis of rotation. For example, if a semicircle rotates around an axis of rotation that passes through the diameter, a cylinder is obtained.

If a parabola is rotated around its axis of symmetry, a form of revolution known as a paraboloid is obtained. It is also important in spherical geometry, where it is used to describe the rotation of the Earth. This line marks the point around which the Earth revolves and around which the Sun, Moon, and other celestial bodies move.

## What are the characteristics of mathematical rotation?

Mathematical rotation is a geometric operation that consists of changing the position of an object around a fixed point. In other words, is the movement given to an object to rotate it around a fixed point. This rotation can have different characteristics that are detailed below:

• Rotation angle: It is the measure in degrees that the object moves around the fixed point. It can be a positive or negative angle, depending on the direction of the rotation.
• The sense of rotation: It can be clockwise or counterclockwise. This is determined by the sign of the angle of rotation.
• The center of rotation: This is the fixed point around which the rotation is performed. The object will move around this center.
• The direction of rotation: Rotation can occur in different directions, depending on the angle of rotation and the direction of rotation.
• The symmetry of the rotation: There can be symmetrical rotations, which maintain the shape and orientation of the object, or asymmetrical, which modify the shape and orientation.
• The periodicity of the rotation: Rotation can be periodic or non-periodic. A periodic rotation repeats the same pattern for each full turn.
• Rotation speed: It refers to the speed with which the object moves around the point of rotation. It can be constant or variable.
• The starting and ending position of the object: Rotation can change the starting and ending position of the object, depending on the angle of rotation and the direction of rotation.

## What is the formula for the axis of rotation?

The formula for calculating the axis of rotation depends on several factors, such as the orientation of the object or the coordinate system used. However, in general, the following formula can be used in Cartesian coordinates: rx F = Iω

where r is the vector from the axis of rotation to the point where force F is applied, I is the moment of inertia (a measure of an object’s resistance to rotation), and ω is the angular velocity (the speed with which an object rotates around its axis). This formula is known as the equation of motion of a rigid body and is used in mechanics to describe how objects that have a definite shape and do not change their shape with movement move.

## Examples of axes of rotation

Here we name you some examples of axes of rotation:

• The Translation of the Earth: This is the main axis of rotation of our planet, which runs through its center from pole to pole.
• A wall clock: The axis of rotation is the axis of the minute hand.
• A ceiling fan: The axis of rotation is the axis that drives the blades.
• A spinning top: The axis of rotation is the axis through the center of the top, around which it rotates.
• A carousel: The axis of rotation is the axis that supports the seats and around which the carousel rotates.
• A metal lathe: The axis of rotation is the axis about which the part being machined rotates.
• A Ferris wheel: The axis of rotation is the axis on which the spoons that carry people are fixed.
• A drill: The axis of rotation is the axis of the bit that is used for drilling.
• A blender: The axis of rotation is the axis of the blades in charge of crushing the food.
• A bicycle: The axis of rotation is the axis of the pedal, around which the wheel rotates when pedaling.