Motion in One Two and Three Dimensions

When a baseball is hit by a bat, what determine where the baseball land? How do you describe the motion of a roller coaster car along a curved track or the flight of a hawk cycling over an open field? If you throw a water balloon horizontally from your window will it take the same amount of time to hit the ground as a balloon when you simply drop?

We can’t answer these kinds of question using the techniques of a motion in a straight line also known as one dimensional motion. Instead we have to confront the reality that our world is three dimensional. To understand the curved flight of a baseball the orbital motion of a satellite or the trajectory of a thrown projectile we need to extend our description of motion to two and three dimensional situations. Will still use the vector quantities displacement, velocity, and but now will have two or three components and will no longer lie along a single line.

When a point object is moving in space, its position at an instant can be described with the help of its three position coordinates (x, y, z), which are changing with time. It may noted that the position of the point object changes even due to a change in one or two of the three position coordinates. Accordingly, we have three types of motion.

One dimensional motion

The motion of an object is said to be one-dimensional motion if only one out of three co-ordinate find the position of the object changes with respect to time.

In such a motion, the object moves along a straight line or a well-defined path. Therefore one dimensional motion is sometimes known as rectilinear or linear motion.

An object moving from point O to point A along x-axis is one dimensional motion.

For example, the motion of a train along a straight railway track, an object dropped from a certain height above the ground, a man walking on a level and narrow road, relations of a mass suspended from a vertical spring, etc. belong to one-dimensional motion.

Two dimensional motion

The motion of an object is said to be two dimensional motion if two out of three co-ordinate define the position of the object change with respect to time. In such a motion, object moves in a plane.

An object moving from point O to point A along xy-plane is two dimensional motion.

For example, an insect crawling over the floor, Earth revolving around the sun, a billiard ball moving over the billiard table etc. belong to this type of motion.

Three dimensional motion

The motion of an object is said to be three dimensional motion if all the three coordinates specifying the position of the object change with respect to time. In such a motion, the object move in a space.

An object moving from point A to point B in which all the three co-ordinates changes is a three dimensional motion.

For example, a kite flying on a windy day, random motion of a gas molecule a flying airplane or bird etc. belong to this type of motion.

To study the motion of an object one has the change in the position of the object with respect to its surrounding with the passage of time. In mechanics (in general) it is specified with the help of a set of three mutually perpendicular line, called the co-ordinate frame.

In the above figure the point A represent the initial position of an object, while the point B represents the final position. Each of the two points of the object is fixed in the space with the help of a set of three distances x, y, and z along x-axis, y-axis and z-axis respectively called co-ordinates of the point. The change in the position of the object with the passage of time means the change in the values of x, y, and z. The position of the object changes due to change in one or two or all the three co-ordinates.

One of the example of three dimensional motion is the projectile motion with no air resistance is a combination of two independent motion. Horizontal motion with constant velocity and verticla motion with constant acceleration. The path of a projectile motion is a parabola.