Rotation around a fixed axis
From The Art and Popular Culture Encyclopedia
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Rotation around a fixed axis is a special case of rotational motion. The fixed axis hypothesis exclude the possibility of a moving axis, and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation around more than one axis at the same time is impossible. If two rotations are forced at the same time, a new axis of rotation will appear.
The kinematics and dynamics of rotation around a fixed axis of a rigid body are mathematically much simpler than those for free rotation of a rigid body; they are entirely analogous to those of linear motion along a single fixed direction, which is not true for free rotation of a rigid body. The expressions for the kinetic energy of the object, and for the forces on the parts of the object, are also simpler for rotation around a fixed axis, than for general rotational motion. For these reasons, rotation around a fixed axis is typically taught in introductory physics courses after students have mastered linear motion; the full generality of rotational motion is not usually taught in introductory physics classes.
In the beginning study of linear motion, objects are treated as point particles without structure; for such objects it does not matter where a force is applied, only that it is applied. However, for extended objects, the point of application of force does matter. In tennis, for example, if a tennis ball is struck with a strong horizontal force acting through its center of mass, it may travel a long distance before hitting the ground, far out of bounds. Instead, the same force applied in an upward, glancing stroke will yield topspin to the ball, which can cause it to land in the opponent’s court.
The concepts of rotational equilibrium and rotational dynamics are also important in other disciplines. For example, students of architecture benefit from understanding the forces that act on buildings and biology students should understand the forces at work in muscles, bones, and joints. These forces create torques, which tell us how the forces affect an object's equilibrium and rate of rotation.
An object remains in a state of uniform rotational motion unless acted on by a net torque. This principle is analogous to Newton's first law of motion. Further, the angular acceleration of an object is proportional to the net torque acting on it, which is the analog of Newton’s Second Law of motion. A net torque acting on an object causes a change in its rotational energy.
Finally, torques applied to an object through a given time interval can change the object's angular momentum. If there are no external torques, angular momentum is conserved, a property that explains some of the mysterious and formidable properties of pulsars—remnants of supernova explosions that rotate at equatorial speeds approaching that of light.
See also
- Artificial gravity by rotation
- Axle
- Carousel, Ferris wheel
- Centrifugal force
- Centrifuge
- Centripetal force
- Circular motion
- Coriolis effect
- Fictitious force
- Flywheel
- Gyration
- Revolutions per minute
- Revolving door
- Rigid body angular momentum
- Rotational speed
- Rotational symmetry
- Spin
