## Motion of a body

Motion of a body can be divided into following types.

### Linear motion

1) It is that motion in which a particle moves along a straight line with respect to a line with respect to a point of reference.

2) A body is said to be in linear motion if every constituent particle of the body move along parallel straight line and covers same distance in the given time.

3) When a force is acting on a body and the body moves in the direction of force, applied then the motion of the body is called linear motion. Example: The motion of a vehicle on a straight road, the motion of a train on straight rails, the motion of a bob of simple pendulum when given small displacement from its equilibrium position and let it go etc, are linear motions.

Note: When an object goes on changing its position with time, with respect to its surroundings then the position of the object at an instant can be described by three positions Coordinates (x, y, z).

### Motion in one dimension

It is that the motion of a body in which a particle or a body moves in one particular direction with respect to a point of reference. It is that the motion of a point mass body in which only one out of the three coordinates specifying the position of the body changes with respect to time. In such a motion, the particle or a body moves along a straight line or a well defined path. Therefore, one dimensional motion is sometime known as rectilinear motion. For Example, the motion of a train along a straight railway track, a body moving vertically downwards from a certain height above the ground, a body moving vertically upwards, oscillations of a mass suspended from a vertical spring etc. belong to one dimensional motion of a body.

### Motion in two dimensions

1) It is that the motion, in which a particle or a body moves simultaneously in two perpendicular directions, with respect to a reference point.

2) It is that the motion of a point mass body, in which two out of the three coordinates specifying the position of body change with respect to time.

3) In such a motion, the particle or a body moves in a plane.

For example, an insect crawling over a floor, the motion of a particle in a circle, a projectile motion when given angular projection with respect to ground etc. belong to two dimensional motion of a body.

### Motion in three dimensions

1) It is that the motion, in which a particle or a body moves simultaneously in three perpendicular directions, with respect to a reference point.

2) It is that the motion of a point mass body, in which all the three coordinates specifying the position of body change with respect to time.

3) In such a motion, the particle or a body moves in a space.

For example, a kite flying on a windy day in space, random motion of a gas molecule in a container, a flying aero plane or birds in space etc. belong to three dimensional motion.

### Projectile

Projectile is the name given to a body thrown with same initial velocity and then allowed to move under the action of gravity alone, without being propelled by any engine or fuel. The path followed by a particle is called its trajectory.

### Periodic motion

It is that motion which is identically repeated after a fixed interval of time. The time interval after which the motion is repeated is called period of motion. For example

1) The revolution of earth around the sun, its period of revolution is one year.

2) The rotation of earth about its polar axis, its period of revolution is 24 hours.

### Oscillatory motion or vibratory motion

1) It is that motion which the body moves to and fro or back and forth repeatedly about a fix point (called mean position), in a definite interval of time.

2) In such a motion, the body of confined within well defined limits (called extreme position) on either side or mean position. For example, the motion of a pendulum of a wall clock is oscillatory motion and the motion of a loaded spring, when the load attached to the spring is pulled once a little from its mean position and left to itself.

### Simple Harmonic Motion

1) It is a special type of periodic motion, in which a particle moves to and fro repeatedly about a mean (i.e. equilibrium) position under a restoring force, which is always directed towards the mean position and whose magnitude at any instant is directly proportional to the displacement of the particle from the mean (i.e equilibrium) position at that instant i.e. F= -ky where k is shown as force constant. Here have sign shows that the restoring force (F) is always directed towards the mean position.

2) The displacement of the particle executing S.H.M. at an instant can be expressed in terms of one single harmonic function (i.e. sine or cosine function). Hence it is called S.H.M.

3) Geometrical interpretation of S.H.M S.H.M is defined as the projection of a uniform circular motion on any diameter of a circle of reference.

4) S.H.M can be linear and angular S.H.M.

5) The linear S.H.M. is always along a straight line about a fixed point on a line, whereas the angular S.H.M. is always along an arc of a circle about a fixed point on the arc.

6) The linear S.H.M. is controlled by force law, where F = -ky where k is the restoring force constant i.e. force per unit displacement. The angular S.H.M. is controlled by torque law.

### Wave motion

Wave motion is a sort of disturbance which travels through a medium on account of repeated periodic vibrations of the particles of the medium about their mean position.