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FUNDAMENTAL PHYSICS: MCU

Circular Motion
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Circular Motion Circular motion is based on an axis of rotation and constant radio: the path be a circle . If, moreover, the speed is constant, occurs uniform circular motion, which is a particular case of circular motion with fixed radius and constant angular velocity.
Table of Contents [hide ]
1 Concepts
1.1 Parallelism LM angular

1.1.1 1.1.2 Arc Angular Speed \u200b\u200b1.2 Speed \u200b\u200b

1.2.1 tangential angular acceleration
2 Period and frequency
3
centripetal acceleration Centripetal force 4
5 See also
/ /

Concepts
The circular motion should be taken into account some specific concepts for this type of movement :
rotation axis: the line around which rotation takes place, this axis can remain fixed or vary over time, but for every moment of time is the axis of rotation. Arco
angular : starting from an axis of rotation is the angle or arc of unit radius with the measured angular displacement. Its unit is the radian . Angular velocity
: is the change in angular displacement per unit time
angular acceleration: the change in angular velocity per unit time
In dynamics of rotating motion also takes into account:
Moment inertia: it is a quality of bodies obtained by multiplying a portion of mass on the distance separating the axis of rotation.
Torque: or torque is the force applied by the distance to the axis of rotation. Parallelism

LM angular linear


angular movement
Arco
position

Speed \u200b\u200bSpeed \u200b\u200b
angular acceleration angular acceleration


Mass moment of inertia

Force Torque

Momentum Angular momentum


Despite the differences, there are certain similarities between the linear and circular, which are worthy of note, and leaves the lights the similarities in the structure and a parallel in the magnitudes . Since an axis of rotation and the position of a particle rotary motion, for a time t, since we have:


Arco Arco angle: angle or position is the arc of circumference, measured in radians, which makes a move, as indicated by the letter:.
If we call and the linear displacement along the circumference of radius r, we have:
.


Angular velocity Angular velocity: Call the angular velocity variation of the arc versus time signal with the letter, and defined as:



tangential speed is defined as the actual speed of the object effected circular motion, if we call VT to the tangential velocity along the circumference of radius r, we have:
.


angular acceleration angular acceleration is defined as the change in angular velocity per unit time and represented by the letter, and is calculated: If we call aa

linear acceleration along the circumference of radius r, we have:
.
Period and frequency

The period indicates the time it takes for a mobile in a walk around the circle goes. Its main formula is:

Frequency is the inverse of the period, ie the turns a mobile unit of time, usually seconds. It is measured in hertz I - 1



centripetal acceleration centripetal acceleration affects a mobile if it performs a circular motion, either uniform or accelerated. The formula to find it is:


centripetal force
Given the mass of the mobile, and based on Newton's second law (F = ma) can calculate the centripetal force which is submitted by mobile following formula:

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FUNDAMENTAL PHYSICS: MATHEMATICS

Parabolic Movement

The composition of a uniform motion and a constant acceleration is a movement whose trajectory is a parabola. MRU
A constant horizontal speed vx.
A vertical MRUA initial velocity going up.
This movement is studied since antiquity. It incorporates the older books ballistics to increase accuracy in the shooting of a projectile. We call
projectile every body that once released it moves only on the acceleration of gravity.
1. Firing projectiles.
consider a cannon fires a shell from the floor (y0 = 0) with angle θ less than 90 ° to the horizontal.
The equations of motion, due to the composition of a uniform motion along the axis X, and a uniformly accelerated motion along the axis, are:
The parametric equations of the trajectory are
x = v0 · cosθ · t = v0 · senθ · t-gt2 / 2
Lost time t, we obtain the equation of
tr .1. Scope.
The horizontal span of each of the projectiles is obtained for y = 0.
Its maximum value is obtained for an angle θ = 45 °, having the same value for θ = 45 + a, that for θ = 45-a. For example, have the same range missiles fired from firing angles of 30 º and 60 º, since sin (2.30) = sin (2.60).

1.2. Maximum height.
The maximum height a projectile is obtained with v = 0.
Its maximum value is obtained for the firing angle θ = 90 °.

1.3 Abstract. Flight time

Maximum range Maximum height

.4. Tyre parabolic initial height.
It fires a projectile from a height h on a horizontal plane with initial speed v0 at an angle θ with the horizontal. To describe the motion establish a reference system as shown in Fig.
The components of the velocity of the projectile as a function of time are:
vx = v0 = v0 · · cosθvy senθ-gd t
The position of the projectile is a function of time ·
x = v0 t = cosθ · h + v0 · senθ · tg · t2 / 2
These are the parametric equations of the trajectory, and that given the time t gives the y position of the projectile.


Proceeding similarly we can derive the equations for the maximum range, maximum height and flight time.
range of a projectile to an initial velocity of 60 m / s and different angles of tiroayectoria (equation of a parabola)