# Spherical body

The way the body is arranged forms a spherical body.  The mind and body are used to form the sphere.  Intention the connection medium between physical and non physical.

A spherical body  is formed.

Taiji is round, never abandoning its roundness whether going in or out, up or down, left or right. And Taiji is square, never abandoning its squareness whether going in or out, up or down, left or right.

As you roundly exit and enter, or squarely advance and retreat, follow squareness with roundness, and vice versa. Squareness has to do with expanding, roundness with contracting. Squareness means a directional focus along which you can express your power.

Roundness means an all-around buoyancy with which you can receive and neutralize the opponent’s power.

The main rule is that you be squared and rounded. After all, could there be anything beyond these things?   By means of this you will become proficient at the skill. But “gazing up, it grows higher, and drilling in, it gets harder”

Ball rotation

The point on the top of the wheel has a speed (relative to the ground) that is twice the velocity of the center of mass.

every point on a non-slipping ball moves at its own speed.

For every point, the motion is made up of rotation and translation.

If the center of the ball with radius RR moves at velocity vv, then the motion of a point at a distance rr can be thought of as the superposition of

• rotation with angular velocity ω=vRω=vR
• translation with velocity vv

Adding these together, a point will move vertically with a sinusoidal motion with amplitude rr and frequency ωω so the velocity will be

vv=ωrcos(ωt)vv=ωrcos⁡(ωt)

the horizontal velocity will be

vh=v+ωrsin(ωt)vh=v+ωrsin⁡(ωt)

This means that the point that is touching the surface is not moving (at that very instant), while the point at the top is moving at twice the speed of the point at the center. All other points are moving at their own velocity.”

The problem that we will likely run into when combining simple shapes is that the equations tell us the rotational inertia as found about the centroid of the shape and this does not necessarily correspond to the axis of rotation of our composite shape. We can account for this using the parallel axis theorem.

The parallel axis theorem allows us to find the moment of inertia of an object about a point ooo as long as we known the moment of inertia of the shape around its centroid ccc, mass mmm and distance ddd between points ooo and ccc.

The parallel axis theorem states that if the body is made to rotate instead about a new axis z′ which is parallel to the first axis and displaced from it by a distance d, then the moment of inertia I with respect to the new axis is related to Icm by
{displaystyle I=I_{mathrm {cm} }+md^{2}.} I=I_{mathrm {cm} }+md^{2}.
Explicitly, d is the perpendicular distance between the axes z and z′.
The parallel axis theorem can be applied with the stretch rule and perpendicular axis theorem to find moments of inertia for a variety of shapes.”

What this means is that a center can be established in another body by displacing that bodies center, the effect one has “inertia” moment must be equal to the distance from the ones own axis.

This illustrates that the point of transference or “moment”  of inertia is at the point of contact provided that a “parallel axis” has been established.  If this is not done one will “miss” the point

Area moment of inertia

“The parallel axes rule also applies to the second moment of area (area moment of inertia) for a plane region D:

where Iz is the area moment of inertia of D relative to the parallel axis, Ix is the area moment of inertia of D relative to its centroid, A is the area of the plane region D, and r is the distance from the new axis z to the centroid of the plane region D. The centroid of D coincides with the centre of gravity of a physical plate with the same shape that has uniform density.”

When we talk of “tingjin”  this is the ability to accurately feel and know where the others center is in respect to one’s own.

Balance

The center of mass (COM) is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero.

the physical state in which all components of a system are at rest and the net force is equal to zero throughout the system

The response [of a system in static equilibrium] to a small perturbation is forces that tend to restore the equilibrium.

Unstable Equilibrium

Unstable Equilibrium
A ball on top of a hill can initially be balanced, but if it moves slightly left or right, it gets pushed further and further away from the initial equilibrium position. This is an example of unstable equilibrium.Our notion of “balance” comes directly from the formulation of equilibrium. For something to be “balanced” means that the net external forces are zero.

For example, a coin could balance standing up on a table. Initially the coin will feel no net external force or torque; it is in equilibrium. But if pushed slightly to the side, it will become “off-balance,” experiencing both a force and a torque causing it to fall to the table.

It might have been initially “balanced” and at equilibrium, but it was an unstable equilibrium, prone to being disturbed.

Source: Boundless. “Stability, Balance, and Center of Mass.” Boundless Physics Boundless, 08 Aug. 2016. Retrieved 31 Jan. 2017 from https://www.boundless.com/physics/textbooks/boundless-physics-textbook/static-equilibrium-elasticity-and-torque-8/stability-75/stability-balance-and-center-of-mass-311-1643/

An object is said to be acted upon by an unbalanced force only when there is an individual force that is not being balanced by a force of equal magnitude and in the opposite direction. Such analyses are discussed in Lesson 2 of this unit and applied in Lesson 3.