Mechanics of the gyroscopic precession and calculation of the Galactic mass

A spinning gyroscope precesses about the vertical due to a torque acting upon the wheel. The torque is generated by the shift of moment of force by gravity and it points to the vertical instead of the tangential direction of precession. This intuition offers an alternative and straightforward view of precession dynamics in comparison with the literature. It also presumes a dynamic balance of momentum between circular motions of the wheel spin and precession. Accordingly, the gyroscopic dynamics is then applied to the study of galactic motion of the solar system in space and the Galactic mass is calculated with the inclusion of gyroscopic effect of the solar planets. Results indicate that the gyroscopic effect of Mercury orbiting around the Sun can increase the calculated Galactic mass by 23% in comparison with the result obtained by the classic approach.

The Split Friction Model - Introducing Mixed Lubrication to Curling

In general, the curling stone is subject to mixed lubrication, resulting in the characteristic Stribeck -curve. As velocity increases, the friction force falls quadratically just to rise linearly yet almost flat after the minimum. In the case of a rotating curling stone this results in a torque. Due to isotropy , the lateral force arises as a delta of asymmetric friction forces opposite to the centripetal forces. \par This in turn allows a split friction model that splits up the quadratic curve into two rather constant values for the friction force on the advancing and the retreating side below a critical velocity difference of these sides: the flee force on the advancing side must not exceed the normal force of the retreating side. Only then a curl can happen. This explains why a stone curls towards the end of the throw. \par Following basic static considerations, the stone may theoretically rest on up to three points during a throw. Each single static case is investigated. These results are discussed with additional heuristic calculations that involve Scratch-Theory. Lastly, the influence of gyroscopic precession yields a graph that reflects established experimental observations: A desired flat curve within deviations ranging from 0.80 to 1.02 meter for up to 20 rotations just to rise linearly up to 2 meters for 80 rotations.

Mechanics of the Gyroscopic Precession and Calculation of the Galactic Mass

A spinning gyroscope precesses about the vertical due to a torque acting upon the wheel. The torque is generated by the shift of moment of force by gravity and it points to the vertical instead of the tangential direction of precession. This intuition offers an alternative and straightforward view of precession dynamics in comparison with the literature. It also presumes a dynamic balance of momentum between circular motions of the wheel spin and precession. Accordingly, the gyroscopic dynamics is then applied to the study of galactic motion of the solar system in space and the Galactic mass is calculated with the inclusion of gyroscopic effect of the solar planets. Results indicate that the gyroscopic effect of Mercury orbiting around the Sun can increase the calculated Galactic mass by 23% in comparison with the result obtained by the classic approach.

Effect of rotation and magnetic field in the gyroscopic precession around a neutron star

General relativistic effects are essential in defining the spacetime around massive astrophysical objects. The effects can be captured using a test gyro. If the gyro rotates at some fixed orbit around the star, then the gyro precession frequency captures all the general relativistic effects. In this article, we calculate the overall precession frequency of a test gyro orbiting a rotating neutron star or a rotating magnetar. We find that the gyro precession frequency diverges as it approaches a black hole, whereas, for a neutron star, it always remains finite. For a rotating neutron star, a prograde motion of the gyro gives a single minimum, whereas a retrograde motion gives a double minimum. We also find that the gyroscope precession frequency depends on the star’s mass and rotation rate. Depending on the magnetic field configuration, we find that of the precession frequency of the gyro differs significantly inside the star; however, outside the star, the effect is not very prominent. Also, the gyro precession frequency depends more significantly on the star’s rotation rate than its magnetic field strength.

Gyroscopic stabilization minimizes drag on Ruellia ciliatiflora seeds

Fruits of Ruellia ciliatiflora (Acanthaceae) explosively launch small (2.5 mm diameter × 0.46 mm thick), disc-shaped seeds at velocities over 15 m s −1 , reaching distances of up to 7 m. Through high-speed video analysis, we observe that seeds fly with extraordinary backspin of up to 1660 Hz. By modelling the seeds as spinning discs, we show that flying with backspin is stable against gyroscopic precession. This stable backspin orientation minimizes the frontal area during flight, decreasing drag force on the seeds and thus increasing dispersal distance. From high-speed video of the seeds' flight, we experimentally determine drag forces that are 40% less than those calculated for a sphere of the same volume and density. This reduces the energy costs for seed dispersal by up to a factor of five.

Rotor Orientation Control Strategy of a Linear Arc-Shaped Induction Motor with Multiple Stators

This paper proposes a rotor orientation control strategy on the large proportion of gyroscopic precession of a linear arc-shaped induction motor with multiple stators, applied to maglev bearings. A physical model of the rotor, considering gravitation, is established via analysis based on rotor dynamics: the kinematic model of the rotor, which is installed vertically, can be simplified as rigid body fixed-point rotation. To complete the dynamic formula, the equivalent circuit of a linear arc-shaped induction motor is transformed into dq0 model by Park transformation, in which the decoupling control of the tangential force and the normal force is determined. Moreover, to realize the control strategy combined air-gap cross feedback with damping method, parameter identification, including no-load test and locked rotor test, is modefied. Therefore, the control strategy, aiming at controlling the speed and guaranteeing the rotor rotating vertically around its axis simultaneously, by adjusting the current of the four stators, can be proved by simulation and experimental platform.

Analogies of Ocean/Atmosphere Rotating Fluid Dynamics with Gyroscopes: Teaching Opportunities

The dynamics of the rotating shallow-water (RSW) system include geostrophic f low and inertial oscillation. These classes of motion are ubiquitous in the ocean and atmosphere. They are often surprising to people at first because intuition about rotating f luids is uncommon, especially the counterintuitive effects of the Coriolis force. The gyroscope, or toy top, is a simple device whose dynamics are also surprising. It seems to defy gravity by not falling over, as long as it spins fast enough. The links and similarities between rotating rigid bodies, like gyroscopes, and rotating fluids are rarely considered or emphasized. In fact, the dynamics of the RSW system and the gyroscope are related in specific ways and they exhibit analogous motions. As such, gyroscopes provide important pedagogical opportunities for instruction, comparison, contrast, and demonstration. Gyroscopic precession is analogous to geostrophic flow and nutation is analogous to inertial oscillation. The geostrophic adjustment process in rotating fluids can be illustrated using a gyroscope that undergoes transient adjustment to steady precession from rest. The controlling role of the Rossby number on RSW dynamics is reflected in a corresponding nondimensional number for the gyroscope. The gyroscope can thus be used to illustrate RSW dynamics by providing a tangible system that behaves like rotating fluids do, such as the large-scale ocean and atmosphere. These relationships are explored for their potential use in educational settings to highlight the instruction, comparison, contrast, and demonstration of important fluid dynamics principles.