Classical Mechanics


Classical Mechanics: It's divided into two main parts. These are 
                              1.Statics
                              2.Dynamics

1.Statics:It's the study of stationary bodies under external forces in macroscopic system. 
2.Dynamics:It's the study of moving bodies under external forces in macroscopic system. It's divided into two subdivisions. 
These are 
                  1.Kinematics
                  2.Kinetics

1. Kinematics:It's the study of moving bodies without causes of motion of the bodies. For example: A body is falling freely from tower. How much distance it traveled? How much its velocity and acceleration? How much its time taken? 
2.kinetics: It's the study of moving bodies with causes of motion of the bodies. For example: A body is falling freely from tower. How can its falling freely ? Which forces acting on it ? A body is at rest means two or more forces are balanced.

A body is at rest on a table. The weight of the body acting on table is equal to a force acting on the body by table. Then the forces are balanced. So, the body is at rest.

Rest and Motion:
When do we say that a body is at rest or in motion? The position of an object changes with respect to surroundings or time, then we say that the body is in "motion". The position of an object doesn't change with respect to surroundings or time, then we say that the body is at "rest". 

             A train is moving with respect to standing person on a platform, the train is at rest with respect to passenger. Which one is correct? Both are correct. So, rest and motion are relative. 
These are dependent on a frame of reference. Frame of reference consists one or more coordinates with a origin. The platform is one frame of reference  and  inside the train is another frame of reference. 

                     A bus is moving along straight road, then how can we find out its postion? How many coordinates  need? We should be need clock and one coordinate i.e., x-axis. Then we can find out the position of the bus.(the bus is started A place at time t1 and after some time t2 the bus reached at B place. The distance between A and B is X km, then the position of the bus is X km at t2.)

Distance
 

Distance
Suppose  a person is at A at time t1 and at B at time t2 with respect to a given frame( see above figure). During the time interval t1 to t2 the body moves along the path ACDEB. The length of the path ACDEB is called the distance travelled by the person. The length of actual path is called distance. Distance has magnitude only and doesn't dependent direction of the person. It's a scalar quantity. It can never be negative or zero  when a person moves some distance any direction. Distance increases with time when a body is moving. S.I.Unit of it is metre(m). C.G.S. Unit of it is centimetre(cm). Biggest unit of distance is kilometre (km).

Displacement 
Displacement

Above figure observe that, if we connect the initial position A with final position B by a straight line, we get the displacement of the person. The shortest distance between initial position to final position is called displacement. It has magnitude as well as direction. It's a vector quantity. It can be negative,  zero or positive. Displacement  can decreases or increases with time when a body is moving. S.I.Unit of it is metre(m), C.G.S.Unit of it is centimetre(cm).

Note: Distance can be equal to or greater than displacement.
Problems 
1. An person moves on a circular ground of radius 30m during a evening walk. If he starts one point A of ground and reaches at another point B, this point exactly opposite to point A.
i) How much distance travelled by the Person? 
ii) How much displacement travelled by the person?
Fig:Distance  and Displacement 

Solution: The person reaches opposite to initial position i.e., the person completed an half of the ground. The distance covered by the person equals the length  of half of the ground. So distance equal to πr=22÷7×30
                                            =94.2 m
T
                           =2r 
                          = 2×30
                          = 60 m
Above question, if he starts one point A and reaches at point A. Then
i) How much distance travelled by the person? 
ii) How much displacement travelled by the person?
Distance and displacement
          Fig:Distance  and Displacement  

Solution : The person reached initial position of the circular ground. So, distance equal to 
                                          =2πr
                             =2×3.14×30
                             = 188.4 m
            
             The displacement is zero.     

          

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