Rotational Dynamics

       

   Physics is a branch of science which deals with the study of secret of matter.

Chapter No:01

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Rotational Dynamics

In our day to day life we come across many interesting activity and we are curious about it, like how sports bike are able to turn at such great speed, how stunt is performed inside well of death (Maut ka kuwa), how top (bhawra) is able to rotate for so long without slipping? and many more.The fact behind all this is Rotational Dynamics.

Rotational stands for a object that is following a circular pattern.

Dynamics stands for  object in motion.

We can further Divide Rotational Dynamics into two parts

1) Circular Motion

2) Rotational Motion

Circular Motion : Motion of a particle which is along circumference of a circle  is known as circular motion.

Let us understand the concept in very simple way by visualization. In the given figure, consider a circle of radius 'r' and point 'O' as centre. Let initially a particle is at position P and it displaces till Q. The distance from P to Q is called as linear displacement. At the same time, the position vector 'OP' and 'OQ' traces an angle  'θ'  between  P to Q at the centre. This is known as Angular displacement.

s : Linear Displacement

θ : Angular Displacement

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Mathematically, 

                           

                                    S =  r θ 

Linear displacement = radius  X  Angular displacement
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Vertical Circular Motion

Motion of a particle along the circumference of a circle  in vertical direction is called  vertical Circular Motion. It is  non Uniform Circular Motion .Velocity of the particle keeps on changing at every instant.

Let us consider a particle at position A at top of  vertical circular motion as shown in fig above,

As it is non uniform circular motion , the velocity of a particle will be different at different point.

Let us find velocity of a particle at A, B , C position as shown in fig.

Velocity at point A

At point A , the force acting on the particle is Weight 'mg' acting vertically downward and Tension 'T' in the string acting Vertically downward as tension always pulls. Both 'T' and 'mg'  balances Centripetal force.

Mathematically , it is given by 

T + mg = mvh2 / r    -------(1)

At point A , at minimum velocity Tension will become zero and string will slack.

Eqn (1) becomes,

0 + mg = mvh2 / r   

g = vh2 / r   

vh2 / r   = g

vh2 = rg   ---------- (A)