MOMENTUM

 

Linear Momentum  of a body (usually called simply its momentum) can be defined as the mass of a body multiplied by its velocity.

 

                   Momentum    =    mass    x    ( distance /  time )

 

                   Momentum   =     mass      x       velocity

 

Units  of momentum are   kg m s-1

 

Angular Momentum is a measure of the difficulty that is experienced in stopping a body.

 

 

NEWTON’S LAWS OF MOTION

 

Newton’s Laws may be stated as follows:

 

1.       A body which has no resultant force on it either remains at rest or moves in a straight line at constant speed.

 

2.       The magnitude of a force is proportional to the rate of change of momentum that it causes.

 

3.       Action and reaction are equal and opposite.

          That is, if a body A is exerting a force on a body B, then B must be exerting an equal and opposite force on A.

 

Newton’s second law may be stated mathematically as follows:

                                                 dv

                              F   =   m .  ___

                                                dt

where          F = force (Newtons)

                   m = mass (kg)

                   v  = velocity  (m/s)

                   t  =  time  (s)

                   a  =  acceleration  (m/s2)

                            

or                              F   =   m  .  a

 

IMPULSE

 

In many practical applications of momentum the force applied will not be constant.  Consider a ball, of mass 0.20kg, travelling with velocity  28 m s-1 directly towards a wall.  It hits the wall and bounces off in the opposite direction with a velocity of 20 m s-1.

 

The change in the ball’s momentum is:

 

Final momentum away from the wall   -   initial momentum away from the wall

 

          =        ( 0.20 kg  x  20 m s-1)  -  (0.20 kg x -28 m s-1)  

          =        9.6  kg m s-1   or   Ns

 

It can be said that the wall has exerted a force on the ball in such a way as to provide the same effect as a constant force of  9.6 N for  1 second.

 

However, this could have been achieved by a force of 96 N for 0.1 seconds or a force of 48 N for 0.2 seconds.

 

The impulse applied to an object will be the measure of the change in momentum of the object.

For a constant force it is the product of Force   x   time.

For a varying force it is the average force    x    time.

 

 

Therefore:             Impulse     =       change in momentum

                     

                             Impulse       =       force  x  time

 

                             Impulse                 =       m .v     -     m. u

 

where     v  is the final velocity  and  u  is the starting velocity.

 

Often the term impulse is used when the force is applied for a brief time, but there is no reason why it cannot be applied when longer times are involved.