Axis of Rotation
The "Axis of Rotation" is a fundamental concept in physics and geometry, referring to an imaginary line around which an object rotates. This axis can either be located within the object itself or external to it. For example, the Earth rotates around an axis that extends through its North and South Poles, while also orbiting the Sun, which represents an external axis. In everyday life, familiar instances of axes of rotation include bicycle wheels and merry-go-rounds, each rotating around a central point.
Understanding axes of rotation is essential in various fields, such as human biomechanics, machine design, and computer graphics. In human movement, joints serve as axes, facilitating the rotation of limbs—such as when you move your arm through different motions. Additionally, the concept plays a crucial role in aviation, where pilots must control an aircraft's movement around three primary axes: pitch, roll, and yaw. Furthermore, the rotation of two-dimensional shapes around an axis can create three-dimensional forms, a principle that is explored in calculus through integration to determine the volumes of these shapes. Overall, the axis of rotation is a key element in both theoretical and practical applications across multiple domains.
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Subject Terms
Axis of Rotation
Rotational movement is defined as movement where all particles of an object move through the same angle in a plane in the same amount of time. The center of rotation is called the axis of rotation. The axis is perpendicular to the plane of motion for the object. See Figure 1 for an example of a single point being rotated about an axis.
The axis of rotation can be on the object or outside the object. For instance, the earth spins about an axis which passes through the North and South Poles (an axis on the object), while also rotating about the Sun (an axis located outside the object). Other examples of axes of rotation in everyday life include the hub or axis of a bicycle wheel. A merry-go-round rotates about its axis of rotation which is a vertical line passing through the center of the merry-go-round. Axes of rotation are important in human movement, machine design, and computer graphics. Flying an airplane requires a deep understanding of rotation about an axis. Axes of rotation can be fixed or movable. An understanding of fixed axes of rotation is important to have before being able to comprehend moving axes.
Overview
In about 400 BC the ancient Greeks believed that the Earth rotated about an axis, later conjecturing that the Earth rotated about the sun. The Wright Brothers designed their early aircraft to include controls that manipulated rotation about three axes. The rotations created by the three axes are called pitch (rotation about axis pointing left and right), roll (rotation about axis pointing from front to back of plane), and yaw (rotation about axis pointing up and down).
Human movement involves rotation about axes through joint centers to create motion. For instance, when you move your arm from your side to in front of you at eye level, you are rotating your arm through an axis that passes through your shoulder joint, between your right and left shoulders. Your shoulder can also rotate about an axis that points forward and backwards, which would move your arm out to the side. A third axis of rotation points up and down and turns your arm inward and outward.
Many three-dimensional shapes are created by the rotation of a two-dimensional shape about an axis. Figure 2 illustrates this concept with the same two-dimensional shape, but different axes of rotation. The line segment (shown with the dark line) in the x-z plane is rotated about the z-axis in the image on the left. The result is a cone with its vertex at the origin and curved surface opened upward. If this same line segment is rotated about the y-axis, another cone is created with its vertex at the origin, but now the curved surface opens to the right. The volume of 3-dimensional shapes created by rotating about an axis can be found by calculus, in particular, using integration.
Bibliography
Hamill, Joseph, Kathleen M. Knutzen, and Timothy R. Derrick. Biomechanical Basis of Human Movement. Philadelphia: Lippincott, 2015.
Kleppner, Daniel, and Robert Kolenkow. An Introduction to Mechanics. Cambridge, UK: Cambridge UP, 2014.
Vince, John. Rotation Transforms for Computer Graphics. London: Springer, 2011.