Rotational Dynamics

                                                            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 A, 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.

Fig A

A) Displacement

s : Linear Displacement

θ : Angular Displacement

Mathematically, 

                           

                                    S =  r θ 

Linear displacement = radius  X  Angular displacement

B) Velocity : If the particle takes time t to move from P to Q , then the velocity of the particle can be given by,

Mathematically,

B) Acceleration : It is the ratio of  change in velocity per unit time.

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As  Angular velocity and angular acceleration is a vector quantity , its direction is along the axis of rotation and it is given by right hand thumb rule.

Direction of angular velocity

│Uniform Circular Motion>>>│

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Reflection of wave

 Reflection of  a light wave on a plane surface

To understand reflection of light on a plane surface in form of wave, let us consider wavefront AB incident on a plane surface  making an angle 'i' with surface as shown in below figure.

In this figure, when wavenormal A is at point D, then wave B reaches at point O.As the both wave is in same medium their velocity is same. Let the velocity of wave is 'v' . After incident on the surface at D the wave startt forming next waveform in the same medium  in forward direction and reaches point F in time 't' covering a distance DF= 'vt' and on the same time the wave at point O moves in forward direction and reaches point C covering a distance of  OC = 'vt' in time 't' .

As wave travel in same medium thus distance covered by wave is given by DF = OC = vt.

Now according to huygens principle , the common tangent FC gives the next wave and thus reflection takes place. 

Now In triangle DFC and Triangle DOC,

 DC = DC --------------( Common side)

 DF = OC  ( Distance tarvelled in same time)

Angle  DFC = Angle DOC --------( each 90)

thus Triangle DFC ∽ Triangle DOC 

 Angle ODC = Angle OCD -------(corresponding angle)

Angle i = Angle r 

When reflection take place Angle i = Angle r

                      │<<<huygens wave theory││ Interference of wave│>>>│

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Quality of Sound

Quality of Sound

Introduction : In previous topic we have discussed about the factors affecting the velocity of a sound. In this topic we are going to discuss which parameter helps in understanding the quality of sound. We are going to discuss more about quality of sound in this topic.

Quality of the sound depends upon major three factors.

a) Pitch : Pitch relates to the sharpness or shrillness of a sound . If the sharpness of the sound is more then sound is said to be highly pitched. The more the frequency ,more is the pitch. For eg. The difference heard in the voice of a women and men is due to difference in pitch. Voice of female is very sharp i,e they have high pitch whereas the voice of men is having low pitch i.e low frequency.

b) Timber : Timber refers to quality of a sound heard by a listener .We are able to guess the difference between the voice when the person is suffering from cold or cough. The quality of sound in a musical instruments are due to mixture of tones and overtones. The sound quality in this context mentioned is called as Timbre.

c) Loudness : Loudness of any sound depends on the intensity of a sound. Intensity of a sound is defined as Sound energy passing through a given a area per unit time.

I = E / At

I = P/A

Where 

I = Intensity

P = Power

A = Area

SI unit of Intensity is Watt / m2

The maximum intensity that any human ear can hear is Imax = 101 Watt / m2

The minimum intensity that any human ear can hear is I0 = 10-12 Watt / m2

Mathematical expression for Loudness of a sound

According to weber fechner,

The loudness (L) of a sound is directly proportional to ( log10 I )

For maximum Loudness,

Lmax ∝ log10 (Imax) -----(1)

For maximum Loudness,

L0 ∝ log10 (I0) -----(2)

From (1) and (2) subtracting

Lmax - L0 ∝ log10 (Imax) - log10 (I0) 

Lmax - L0 = K log10 (Imax) - log10 (I0) 

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