CIRCULAR MOTION

CIRCULAR MOTION

Circular and Simple Harmonic Motion
Motion can be defined as a change of position of a body with time. It also involves how things move and what makes them move.

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation.

The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body.

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Examples of circular motion include: an artificial satellite orbiting the Earth at constant height, a stone which is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechanism.

Uniform Circular Motion
Uniform circular motion describes the motion of a body traversing a circular path at constant speed. The distance of the body from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity is not constant. Velocity which is a vector quantity depends on both the body's speed and its direction of travel.

This changing velocity indicates the presence of acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation.

This acceleration is, in turn, produced by a centripetal force which is also constant in magnitude and directed towards the axis of rotation.

In the case of rotation around a fixed axis of a rigid body that is not negligibly small compared to the radius of the path, each particle of the body describes a uniform circular motion with the same angular velocity, but with velocity and acceleration varying with the position with respect to the axis.

Non-uniform Circular Motion
Non-uniform circular motion is any case in which an object moving in a circular path has a varying speed.

The tangential acceleration is non-zero; the speed is changing. Since there is a non-zero tangential acceleration, there are forces that act on an object in addition to its centripetal force which is composed of the mass and radial acceleration.

These forces include weight, normal force, and friction. In non-uniform circular motion, normal force does not always point in the opposite direction of weight.

Since the object's velocity vector is constantly changing direction, the moving object is undergoing acceleration by a centripetal force in the direction of the center of rotation.

Without this acceleration, the object would move in a straight line, according to Newton's laws of motion.

Differences from uniform circular motion
The way to express non-uniform circular motion is not that different from the techniques used in calculating uniform circular motion.

In uniform circular motion, the magnitude of the tangential acceleration is always equal to zero assuming speed remains constant.

The radial acceleration in uniform circular motion is equal to the centripetal acceleration, which is towards the center of the circle. In non-uniform circular motion, the radial acceleration is the same and equal to towards the center of the circle.

What's different is the tangential acceleration, since speed is non-zero and changing.

Since there is a non-zero tangential acceleration, there are forces that act on an object in addition to its centripetal force (composed of the mass and radial acceleration).

These forces on the object include forces such as weight, normal force, and other forces acted on the object due to the environment it is in such as friction.

Simple Harmonic Motion
We have studied linear and circular motions extensively. Right now we will look at oscillation. Oscillating motion is quite complex compare to linear motion but we will try and simplify it so that it will be quite easy to understand.

We will also take a look at a special kind of oscillation called simple harmonic motion.

If you have not heard of oscillation before in physics do not worry because you will soon realized that it all around us.

An oscillatory system can be simply define as a system where by a particle moves back and forth. The particle will always come back to its starting position to make a complete oscillation.

This type of oscillating motion is also called a periodic motion.

Unlike in other kinds of motions, in oscillating motion, amplitude, period, and frequency are used to describe the periodic nature of an oscillating motion.

Time Period
Time period is measured in seconds and it is the time taken for an oscillating object to complete a full cycle. There are situations where by many cycles are complete on a specific time, in order to get the time period of the oscillation, the following formula is used.

T (Time Period) = Time in seconds / Number of oscillation

Frequency of Oscillation
The frequency of oscillation is the number of complete oscillating cycle completed in a second. The frequency of oscillation is related to the period by the following equation.

Frequency = 1 / Time Period

The displacement of an oscillating particle is the distance the particle has been moved from its equilibrium position.

The amplitude of an oscillation is the maximum displacement of the vibrating object from the equilibrium position.

There are many examples of simple harmonic motions in real life but one example we will emphasize on is the simple pendulum. When a pendulum is attached on a string and the other end of the string is attached to a top beam, when the pendulum ball is swing sideways, it exhibits a simple harmonic motion.

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When the pendulum ball moves to it central point – which is consider as the equilibrium point, there is no resultant force on the object. At the far-end, the pendulum ball stops before it changes direction. At this point the velocity of the pendulum is zero and the displacement is at its maximum.

The diagram below shows a graphical representation of simple harmonic motion.

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Simple harmonic motion equations can be used to find different parameters of the motion.

Where V = velocity, A = acceleration, E = energy

Y = A sin wt = A sin √ (Kt / m)

V = wAcos wt

A = - w2Asin wt = -w2y

E = KE + PE = 1/2kA2