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Angular Mechanics

A diagram of angular momentum. Showing angular velocity (Scalar) and radius.

Angular mechanics is a field of Mechanics which studies rotational movement. It studies things such as angular momentum, angular velocity, and torque. It also studies more advanced things such as Coriolis force and Angular aerodynamics. It is used in many fields such as toy making, aerospace engineering, and aviation.

Applications

Aviation

In aviation, angular mechanics is used galore. Propellers spin, which generates angular momentum. Because of the momentum, it directs the air back and keeps the plane up while also propelling it forward. This uses angular mechanics, especially torque and angular momentum.

Toy making

Many toys are made with angular mechanics in mind. These toys include gyroscopes, tops, and yo-yos. When you spin a toy, you apply force to both sides (Push and pull respectively). This makes the top spin. According to newtons third law of motion, the top would continue to spin until a force is acted upon it. Because of all of the forces cancelling out gravity, it will stay upright.

Aerospace engineering

A picture of the international space station.

In aerospace engineering, angular mechanics is put to mind. Where the ISS is located, there is around 90% the gravity of the ground. The reason the ISS does not fall down is due to angular momentum.

Equations

In angular mechanics, there are many equations. Most of which explain the nature of rotational movement.

Torque

The equation for torque is very important in angular mechanics. Torque is rotational force and is determined by a cross product. This makes it a pseudovector.

$\tau =r\times f$

where $\tau$ is torque, r is radius, and $\times$ is a cross product. Another variation of this equation is:

$\tau =rF\sin(\theta )$

Where $\tau$ is torque, r is radius, F is force and $\theta$ is the angle between the two vectors.

Angular velocity

The equation for angular velocity is widely used in understanding rotational mechanics.

$\omega =d\theta /dt$

where $\omega$ is angular velocity and $\theta$ is angle.

Angular acceleration

$\alpha =d\omega /dt$

where $\alpha$ is angular acceleration, and $\omega$ is angular velocity

Planetary motion

When planets spin, they generate angular momentum. This can do things such as cause the planet to be slightly oval-shaped, and cause deformities in the planet. Another example of angular mechanics in planetary motion is orbiting around a star. Because of the speed of the orbit, they do not go plummeting into their star.

Earth

The earth moves 1667.9239 kilometers per hour around its axis. Because of this, you weigh less on the equator than the north pole due to the Coriolis effect. Another thing caused by the Coriolis effect on earth is the deformation of the earth. Because of this, you are farther from the center of the earth on the equator than the north pole. The orbital speed of the earth is about approximately 30 (More precisely, 29.80565528) kilometers per second. This causes the earth to perfectly orbit the sun.

Moon

An example of tidal locking.

The moon orbits the earth at around a kilometer a second (or more specifically, 0.9204818658 km/s). But it is also tidally locked. It generates enough rotational momentum to be at the exact distance that it rotates as fast as it spins.

History

Angular mechanics has a rich history.

~500 BCE-323 BCE

In ancient Greece, people were found playing with yo-yos. Whilst the ancient Greeks did not know much about angular momentum, they were fascinated by its ability to stand up while spinning.

~1295-1358

Jean Buridan, French philosopher discovered momentum, including angular momentum in his lifetime.

~1642-1727

When Isaac Newton discovered his laws of motion, other people built off his laws to make the laws of rotation.

1743

Inspired by the laws of rotation, John Serson invented the gyroscope in 1743.

Rotational laws

Eulers second law

Eulers second law states that the rate of change of rotational momentum about a point that is fixed at any inertial reference frame is equal to the sum of any external torques acting on that body at that point in space

Newtons laws of motion

Newtons laws of motion can translate to rotational laws.

First law

An object at rest tends to remain at rest, but an object in rotational motion will keep rotating unless a force is acted upon it.

Second law

Angular acceleration is equal to the net torque and inversely proportional to the moment of inertia.

Third law

For every action there is an equal and opposite reaction.