Motion in One, Two and Three DimensionsA body is said to be in motion if its position changes with respect to its surrounding. In order to completely describe the motion of such objects, we need to specify its position. For this, we need to know the position coordinates. In some cases, three position coordinates are required, in some cases two or one coordinate is required. Based on these, motion can be classified as

One dimensional motion

Two dimensional motion

Three dimensional motion

Motion in one dimension

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It is also known as rectilinear or linear motion. A particle moving along a straight line is said to undergo one dimensional motion. In such a case, only one of the three rectangular coordinates changes with time.

For example, if we consider one dimensional motion along the X-axis, then when the particle moves from A to B, as shown in the figure below, the X coordinate changes from x1 to x2.

The straight line along which one dimensional motion takes place may be taken either along the X, Y or Z-axis.

Examples of one dimensional motion are:

Motion of a train along a straight line

An object, like a ball, falling freely, vertically under gravity

The vertical up and down oscillations of an object suspended from a vertical spring.

Motion in two dimensions

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A particle moving along a curved path in a plane has two dimensional motion. The figure below, illustrates a two dimensional motion, where a particle moves from P (x1, y1) to Q (x2, y2) along a curved path.

Examples of two dimensional motion are:

an insect crawling on a ball or a globe

a satellite revolving round the Earth

projectile motion, i.e., the two dimensional motion of a particle thrown obliquely into the air, like a baseball or a golf ball as shown below.

The bob oscillates along a curved path if the simple pendulum is oscillating in a vertical plane (as shown in the figure), with a large amplitude. However, for small amplitudes, the bob approximately oscillates along a straight line, i.e., one dimensional motion.

Motion in three dimensions

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A particle moving in space has three dimensional motion.

In this type of motion, all the three rectangular coordinates change with time. The figure above illustrates this type of motion where the particle moves from A to B and the corresponding rectangular coordinates change from (x1, y1, z1) to (x2, y2, z2).

Examples of three dimensional motion are:

A bird flying in the air

A kite flying in the air

Motion in a circle or circular motion is found in many situations in our daily life, such as a roller coaster traveling near the top or bottom of its track, a car traveling around a turn, the Earth orbiting the Sun and a centrifuge. An object with uniform circular motion travels in a circle with a constant speed. If a golf ball tied to a string is whipping around in circles. The ball is traveling at a uniform speed as it follows a circular path, so we can say that it is moving in uniform circular motion. The given figure illustrate the circular motion.

Centripetal Acceleration

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An object moving with a constant speed in a curved path changes its direction of velocity continuously. Because of the velocity changes, acceleration is produced. The direction of velocity of an object which exhibits the uniform circular motion is along the tangent to the

circular path. The changes in the direction of velocity is towards the center of the circular path. So,the centripetal acceleration is defined as the acceleration of an object which is in circular motion and the direction of the acceleration is towards the center of the circular path. Centripetal The meaning of centripetal is 'towards the center' . The mathematical expression for centripetal acceleration is given as,

a= v2

r

Centripetal Force

The centripetal acceleration is produced by a force directed toward the center of circular motion termed as the centripetal force. If Fc represents centripetal force and m be the mass of an object in uniform circular motion, then the mathematical equation for centripetal force is,

Fc = ma Fc ¿m

v2

r

A projectile is an object upon which the only force acting is gravity. There are a variety of examples of projectiles.

An object dropped from rest is a projectile (provided that the influence of air resistance is negligible). An object that is thrown vertically upward is also a projectile (provided that the influence of air resistance is negligible). And an object which is thrown upward at an angle to the horizontal is also a projectile (provided that the influence of air resistance is negligible). A projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity.

Here a welder cuts holes through a heavy metal construction beam with a hot torch. The sparks generated in the process follow parabolic path.  

Projectile Motion Definition

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Projectile motion is an example of curved motion with constant acceleration. It is two dimensional motion of a particle thrown obliquely into the air.

Consider the motion and path followed by the ball when it moves in the curved path. We will make two assumptions here:

a) First assumption is that the free fall acceleration (g) remains constant and does not change its value during the motion of the ball.

b) Resistance offered by the ball is negligible.

If we consider the motion and the assumptions stated above, we will find that :

1. The path of the projectile (ball here) is always a parabola. 2. The path followed by the projectile is termed as the "trajectory of the projectile".3. Projectile feels only one force while in motion, which is the force of gravity.

Projectile Motion is Caused by?

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Projectile motion is caused by the gravitational force of earth.There could be different projectile motions,

An object thrown from a hill to the downward direction, considering that initially the object was at rest, is a projectile motion. We are not considering the effect of the air resistance here. Object will fall down towards the center of the earth due to the force of the gravity.

An object thrown from the ground towards the sky or in the upward direction, follows the projectile motion. Initially a force is applied to the object and its initial velocity is not zero. We are not considering the effect of air resistance here.

An object, thrown towards the sky but by making some angle with horizontal surface, follows the curved path and also the projectile motion. Here also we are neglecting the effect of air resistance.

Figure 1: General Trajectory of the Projectile

The fundamental principle to be understood concerning satellites is that a satellite is a projectile

Once launched into orbit, the only force governing the motion of a satellite is the force of gravity.

It so happens that the vertical distance that a horizontally launched projectile would fall in its first second is approximately 5 meters (0.5*g*t2). For this reason, a projectile launched horizontally with a speed of about 8000 m/s will be capable of orbiting the earth in a circular path. This assumes that it is launched above the surface of the earth and encounters negligible atmospheric drag. As the projectile travels tangentially a distance of 8000 meters in 1 second, it will drop approximately 5 meters towards the earth. Yet, the projectile will remain the same distance above the earth due to the fact that the earth curves at the same rate that the projectile falls. If shot with a speed greater than 8000 m/s, it would orbit the earth in an elliptical path.