Kinetics Of A Particle: Force & Acceleration

Kinetics:

It is the branch of dynamics that deals with the relationship between the change in motion of a body the cause which changes it.

• The base of kinetics is Newton's Second law of motion (F = ma).
• Theory of Relativity  →  placed limitations on 2nd law of motion for describing particle motion.
• Equations of motion fails to predict exact behavior of particle when it reaches speed of light  0.3 Gm/s.

There are two types of diagram which are described as follows:

1. Kinetic Diagram  →  shows inertial forces or net forces of body.
2. Free Body Diagram (FBD)  →  show all external forces on body.

• If inertia force vector is treated in the same way as force vector  →  Equilibrium state is called Dynamic Equilibrium.

There are two types of frame of references but we are discussing only one which is:

• Newtonian or Inertial Frame of Reference  →  state of rest or uniform velocity. Newton's laws only valid for non-rotating and non-accelerating reference system which is translating with constant velocity.

General Procedure For Problem Solving:

1. Select a convenient inertial coordinate system which can be rectangular, normal and tangential or cylindrical coordinates.
2. Draw FBD showing all external forces.
3. Draw the kinetic diagram showing inertia force, ma.
4. Apply equations of motion in scalar form.
5. Identify the unknowns and solve equation.
6. Kinematic relation may be applied

Equation Of Motion For a System Of Particles:

Equation of particle is valid for isolated system. Important points are:

• Only for inertial frame of references.
• Unbalanced force cause acceleration.
• Inertial frame of reference does not rotate.

Applying equation of motion:

• Mass  →  resistance to change in velocity (absolute quantity).

1. Using Rectangular Coordinates:

Use rectangular coordinates for finding the net force having known particle locus. 

Applying equation of motion, we get:

2. Using Normal & Tangential Coordinates:

Use normal and tangential coordinates for particle kinetic analysis when path is known. 

Applying equation of motion, we get:

3. Using Cylindrical Coordinates:

When all the forces acting on the particle can be resolved into cylindrical components easily.

Applying equation of motion, we get:

• Frictional force always act along tangent in opposite direction.

The angle between tangent and radial line is given by:

• Force on a system of particle is totally described as:

References:

• Material from Class Lectures + Book named Engineering Mechanics Statics & Dynamics by R.C. Hibbeler (12th Edition) + from YouTube channel named Yiheng Wang for Engineering Dynamics Mechanics + my knowledge. 
• Pics and GIF from Google Images.  
• Videos from YouTube.