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ANGULAR MOTION FREE

When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum.

ANGULAR MOTION FREE

It is a spinning wheel or disc in which the axis of rotation (spin axis) is free to assume any orientation by itself. Thumbnail: A gyroscope is a device used for measuring or maintaining orientation and angular velocity. Consider a mass m m attached to one end of a massless rod. How does rotational inertia relate to Newton's 2 law Rotational inertia takes the place of mass in the rotational version of Newton's 2 law. If the gyroscope is not spinning, it acquires angular momentum in the direction of the torque, and it rotates about a horizontal axis, falling over just as we would expect. Figure 1: A tethered tennis ball rotating about a central point.

11.5: Precession of a Gyroscope When a gyroscope is set on a pivot near the surface of Earth, it precesses around a vertical axis, since the torque is always horizontal and perpendicular to the angular momentum vector.

The angular momentum of all bodies in the system must be taken about a common axis. Systems containing both point particles and rigid bodies can be analyzed using conservation of angular momentum. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the angular velocity must increase to conserve angular momentum.

11.4: Conservation of Angular Momentum In the absence of external torques, a system’s total angular momentum is conserved.

A rigid rotating body has angular momentum directed along the axis of rotation. The net torque on a system about a given origin is the time derivative of the angular momentum about that origin. For the rotation scheme proposed, the rotation along the z axis occupies most time of one period.

11.3: Angular Momentum The angular momentum of a single particle about a designated origin is the vector product of the position vector in the given coordinate system and the particle’s linear momentum. However, the angular motion makes the rotation scheme become different from the static base, which will cause extra errors and break the modulation law.

Energy conservation can be used to analyze rolling motion since energy is conserved in rolling motion without slipping. In rolling motion with slipping, a kinetic friction force arises between the rolling object and the surface.

The linear velocity, acceleration, and distance of the center of mass are the angular variables multiplied by the radius of the object. 11.2: Rolling Motion In rolling motion without slipping, a static friction force is present between the rolling object and the surface.The small rotors at the tail of the aircraft provide a counter thrust against the body to prevent this from happening, and the helicopter stabilizes itself. The body of the helicopter tends to rotate in the opposite sense in order to conserve angular momentum. The lift blades spin about a vertical axis through the main body and carry angular momentum. 11.1: Prelude to Angular Momentum A helicopter can be used to illustrate the concept of angular momentum.