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## Definitions and concepts of Circular motion

### Definition of Circular motion

In kinematics, the circular motion (also called circumferential movement) is which is based on an axis of rotation and radio constant, so the path is a circle. If, in addition, the rotational speed is constant (wave-like rotation), produces uniform circular motion, which is a particular case of circular motion, with radio and fixed Centre and angular velocity constant.Circular motion should take into account some of the concepts that would be Basic for the description kinematics and dynamics of the same:

• Axis of rotation: is the straight line around which the rotation is performed, this axis can remain fixed or vary over time but for every particular instant is the axis of rotation (in this case considering a differential or infinitesimal variation of time). The rotation axis defines a point called the center of rotation of the described path (O).

• Bow: on the basis of a fixed Center or fixed rotation axis, it is the area covered in the circular path or arc of unit RADIUS with which the angular displacement is measured. Its unit is the radian (travel space divided between the radius of the path followed, division of length between length, dimensionless therefore).

• Angular velocity: is the variation of the angular displacement per unit time (lowercase omega).

• Angular acceleration: is the variation in the angular velocity per unit time (lowercase alpha).

Dynamics of curved, circular or rotating movements also the following quantities are taken into account:

• Angular momentum (L): is the magnitude that is equivalent to the linear time or amount of movement in the rectilinear motion but applied to the curvilinear, circular or rotating movement (vector product the amount of movement by the position vector from the center of rotation to the point where the point mass is located).

• Moment of inertia (I): is a quality of which depends on its shape and the distribution of its mass and bodies which is of a specific portion of the mass multiplied by the distance between the axis of rotation.

• Force moment (M): or torque is the force applied by the distance from the axis of rotation (is the equivalent to the agent force of movement that changes the State of a rectilinear motion).

### Concept of Circular motion

You are defined as a circular motion as those whose trajectory is a circumference.The circular, called also curvilinear movement, is another type of simple movement.

We are surrounded by objects that describe circular motion: a compact disc during playback in stereo, the hands of a clock or a motorcycle wheels are examples of circular motion; in other words, of bodies that move describing a circumference.

Sometimes the circular motion is not complete: when a car or any other vehicle takes a curve made a circular motion, although it never rotates 360 ° of the circumference.

Experience tells us that everything is spinning has circular motion. If that revolves always gives the same number of turns per second, we say that it possesses uniform circular motion (MCU).

Examples of things that move with uniform circular motion there are many:

The Earth is one of them. It always gives one revolution on its axis every 24 hours. It also rotates around the Sun and turns every 365 days. A fan, a washing machine or old turntables, the wheel of a car that travels with constant velocity, are other examples.

But we must not forget that there are also objects that rotate in circular motion varied, either accelerated or decelerado.

The circular motion in angular quantities

The description of a circular motion can do well based on magnitudes linear ignoring the shape of the trajectory (and we will have tangential velocity and acceleration), either on the basis of angular quantities (and will have angular speed and acceleration). Both descriptions are interrelated by the value of the radius of the circumference trajectory.

Working with angular quantities is essential to understand concerning an angle known as the radian unit.

Radian

If we have any angle and want to know how much measured, we take a conveyor and measure it. This gives us the angle, measured in degrees. This method comes from dividing the circumference into 360 °, and is called the sexagesimal.

(To use the calculator in degrees should starting SDRS, Degrees, which means grades in English).

The system of degrees is a way of measuring angles, but there are other methods, and one of them is using radians.

Now let's look at the issue of measuring angles in radians.

To measure an angle in radians is measured the length of the arc (s) covered by the angle θ of the figure to the left. This can be done with a centimeter, by a thread or whatever. The radius of the circle is also measured.

To obtain the value of the angle (θ) in radians, we use the formula:

and we have the angle measured in radians

Make the arc over RADIUS division means to see how many times the radio enters the arc. RADIUS and arc should be measured in the same unit, radian turns out to be a number without units.

This means that the value of the angle in radians only tells me how many times the radio enters the arc. For example, if angle θ measured 3 radians, that means that the radio enters the arc encompassed by that angle 3 times.

Her we would like to calculate or know the value of the arch, we:

### Definition of Circular motion

Uniform Circular motion is described with the same characteristics as the uniform rectilinear motion, the only difference is that this is done in a straight line, while the MCU describes a circular path, this means that the movement that is running is constant in terms of speed and acceleration which is null, however the direction taken in study object is different in the presence of a curved path together in their tips.Unlike the MRU uniform Circular motion works with variable and data according to the circle in which we study, we then rely on the ratio of the angle that takes the particle in motion about the center of origin which is located in the center of the circle. In MCU is used as unit to define the offset a call Radian, which describes a distance that travels all around than the circumference. Uniform Circular motion must be plotted on a Cartesian plane, however the curve should be expressed in terms of radians, fundamental versores (0, I, J) are responsible for measuring the angle and amplitude of this on the circumference.

The angle must be measured in radians, however trigonometry plays a key role in simplifying the result, this angle can also be measured in degrees which I use that it can be given to grades with designed thanks to the complex. In this way we can be with the following data: the entire circumference measured a total of (2Pi) 2π radians or what is equal 360º since π (Pi) in this field unit equals 180 °, average circumference equals 1π, or what is the same 180 °, a quarter circumference can denote it as 90 ° or π/2 and so on until we have with help of trigonometry in a full field of angles for the study. In daily life this movement has a very diverse, application of those objects that describe a lap of constant speed, such as a Ferris wheel, an oven dish microwave, among others.