physics-class-11-unit-05-chapter-06-laws-of-motion-newtons-second-and-third-laws-of-motion-l-6-8-xztj66qeaju

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's First Law of Motion </primary>
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- <span style="color:green"> $1^{st}$ Law</span>: If a body is at rest or moves with uniform velocity (constant speed along the same direction), net force acting on the body =0

- <span style="color:blue"> LAW OF INERTIA</span>

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<footer style = "font-size: 18px"> $\rightarrow$ Laws of Motion $\rightarrow$ <span style = "color:blue"> Newton's First Law of Motion </span> $\rightarrow$ Reference Frame $\rightarrow$ Inertial Frame </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Reference Frame </primary>
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- State of motion $\rightarrow$ <span style="color:green">Dependent on reference frame.</span>

- Force $\rightarrow$ <span style="color:blue">Frame indepandent.</span>

- <span style="color:green"> Newtons $1^{st}$ Law (even $2^{nd}$ law)</span>

- Valid only if we are observing the state of motion from an initial.

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<footer style = "font-size: 18px">Laws of Motion $\rightarrow$ Newton's First Law of Motion $\rightarrow$ <span style = "color:blue"> Reference Frame </span> $\rightarrow$ Inertial Frame $\rightarrow$ Constant Velocity </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Rest Frame </primary>
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- Look at person standing on train.

- <span style="color:green">Frame 1</span>: We fix the axis on ground.

- <span style="color:green">Frame 2</span>: We are fixing the axis on the train compartment and the person is standing at a state of rest.
 
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<footer style = "font-size: 18px">Inertial Frame $\rightarrow$ Constant Velocity $\rightarrow$ <span style = "color:blue"> Rest Frame </span> $\rightarrow$ Reference Frame $\rightarrow$ Reference Frame </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Reference Frame </primary>
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- Let the train accelerate.

- W.r.t. frame 1, person is moving, and has acceleration a.

- With respect to frame two (<span style="color:blue">on train</span>) person is still at rest.

- Inertial frame = <span style="color:green">frame 1</span>

- Accelerating, non inertial frame = <span style="color:green">frame 2</span>
 
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<footer style = "font-size: 18px">Constant Velocity $\rightarrow$ Rest Frame $\rightarrow$ <span style = "color:blue"> Reference Frame </span> $\rightarrow$ Reference Frame $\rightarrow$ Inertal Frame </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Reference Frame </primary>
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- a=0

- v = <span style="color:green">Constant</span>

- If <span style="color:blue">$\vec{a}$=0</span>, train moves in straight line with constant speed then both 1 and 2 are inertial frames.

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<footer style = "font-size: 18px">Rest Frame $\rightarrow$ Reference Frame $\rightarrow$ <span style = "color:blue"> Reference Frame </span> $\rightarrow$ Inertal Frame $\rightarrow$ Rotation of Earth </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Rotation of Earth </primary>
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- We fix a reference frame on center of the earth.

- Is this inertial frame?

- Orbit around sun

- <span style="color:green">Acceleration of the frame fixed to center of earth.</span>

- $\omega_1=\frac{2 \pi}{365 \times 24 \times 3600}$

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<footer style = "font-size: 18px">Inertal Frame $\rightarrow$ Rotation of Earth $\rightarrow$ <span style = "color:blue"> Rotation of Earth </span> $\rightarrow$ Rotation of Earth $\rightarrow$ Frames </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Rotation of Earth </primary>
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- $\omega_1=\frac{2 \pi}{365 \times 24 \times 3600} \mathrm{sec}$

- $\vec{a}=R_1 \omega^2=0.006 \frac{\mathrm{m}}{\mathrm{s}^2}$

- So, theoretically, a frame connected to the center of the earth and rotating with the earth is not an inertial frame.

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<footer style = "font-size: 18px">Rotation of Earth $\rightarrow$ Rotation of Earth $\rightarrow$ <span style = "color:blue"> Rotation of Earth </span> $\rightarrow$ Frames $\rightarrow$ Inertal Frame </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Frames </primary>
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- Fix a frame on centre of sun.

- Sun is moving around centre of galaxy.

- $a_{sun}$ towards <span style="color:green">centre of galaxy</span>

- $=3 \times 10^{-10} \frac{\mathrm{m}}{\mathrm{s}^2}$

- Fix frame to centre of galaxy.

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<footer style = "font-size: 18px">Rotation of Earth $\rightarrow$ Rotation of Earth $\rightarrow$ <span style = "color:blue"> Frames </span> $\rightarrow$ Inertal Frame $\rightarrow$ Newtons Second law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Inertal Frame </primary>
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* Galaxy may be moving towards other galaxies
* If inertal frame exists?
* Cannot be answered
* For most applications in classical mechanics a frame fixed on surface of earth can be treated as inertal frame
* In some case frame fixed to centre of earth is more accurate

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<footer style = "font-size: 18px">Rotation of Earth $\rightarrow$ Frames $\rightarrow$ <span style = "color:blue"> Inertal Frame </span> $\rightarrow$ Newtons Second law $\rightarrow$ Momentum </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Momentum </primary>
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- <span style="color:green">$\vec{p}=m \vec{v}$</span>

- Where
- $\vec{p}$ = Momentum
- m = Mass
- $\vec{v}$ = Velocity

- <span style="color:blue">If we apply the same force on</span>

- A light body $\rightarrow$ Moves faster.

- Heavy body $\rightarrow$ Moves slower.

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<footer style = "font-size: 18px">Inertal Frame $\rightarrow$ Newtons Second law $\rightarrow$ <span style = "color:blue"> Momentum </span> $\rightarrow$ Momentum $\rightarrow$ Stone Tied to a String </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Momentum </primary>
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- Speed is also another factor.

- <span style="color:blue">Let us think of a bullet. </span>

- A bullet fired from a gun hits a target.

- It pierces through the target.

- Same bullet if I take it in my hand and I throw it on the wall, it hits lightly.

- Momentum is define as mass times the velocity.

- Momentum = <span style"color:green">m$\vec{v}$</span>

- Directional effect $\rightarrow$ <span style="color:blue">$\vec{v}$ vector</span>

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<footer style = "font-size: 18px">Newtons Second law $\rightarrow$ Momentum $\rightarrow$ <span style = "color:blue"> Momentum </span> $\rightarrow$ Stone Tied to a String $\rightarrow$ Newton's Second Law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Stone Tied to a String </primary>
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- Angular velocity is constant.

- The stone moves with a constant speed but its velocity is changing.

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<footer style = "font-size: 18px">Momentum $\rightarrow$ Momentum $\rightarrow$ <span style = "color:blue"> Stone Tied to a String </span> $\rightarrow$ Newton's Second Law $\rightarrow$ Newton's Second Law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's Second Law </primary>
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- <span style="color:green">$\vec{F}$</span> acts on a body for time <span style="color:green">$\Delta t$</span>,

- Say the body has a mass $m$, and because of the action of this force, it changes the velocity of the body.

- ${\vec{v}}$ to $\vec{v}+\Delta \vec{v}$.

- <span style="color:blue"> $\vec{p_{initial}}=m \vec{v}$</span>

- $\vec{p_{final }}=m(\vec{v}+\Delta \vec{v})$

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<footer style = "font-size: 18px">Stone Tied to a String $\rightarrow$ Newton's Second Law $\rightarrow$ <span style = "color:blue"> Newton's Second Law </span> $\rightarrow$ Newton's Second Law $\rightarrow$ Newton's Second Law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's Second Law </primary>
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- $\Delta \vec{p}$ = <span style="color:green">Change in momentum</span>

- $\vec{p_{\text {final }}}-\vec{p_{\text {inital }}}= m(\vec{v}+\Delta \vec{v})-m(\vec{v}) = m \Delta \vec{v}$

- <span style="color:blue">Force $\propto \frac{\Delta \vec{p}}{\Delta t}$</span>

- $\Rightarrow \vec{F}=k \frac{\Delta \vec{p}}{\Delta t}$

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<footer style = "font-size: 18px">Newton's Second Law $\rightarrow$ Newton's Second Law $\rightarrow$ <span style = "color:blue"> Newton's Second Law </span> $\rightarrow$ Newton's Second Law $\rightarrow$ Newton's Second Law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's Second Law </primary>
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- In $\text{limit}_{\Delta t} \rightarrow 0$

- $\vec{F}=k \cdot \frac{d \vec{p}}{d t}$

- $\frac{d \vec{p}}{d t}=\frac{d}{d t}(m \vec{v})$

- <span style="color:blue">If m is fixed</span>

- $\frac{d \vec{p}}{d t}=m \frac{d \vec{V}}{d t}=m \vec{a}$

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### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's Second Law </primary>
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- $\vec{F}=k \frac{d \vec{p}}{d t}=k m \vec{a}$

- We choose units of force in such a manner that k=1

- **SI units:**

- m $\rightarrow$ kg

- $a \rightarrow \mathrm{m} / \mathrm{s}^2$

- <span style="color:green">$\vec{F} \rightarrow$ Newtons</span>, $1 N=1 \mathrm{~kg} \frac{\mathrm{m}}{\mathrm{s}^2}$

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### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's Second Law </primary>
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- 1 newton is the force which causes a mass of 1 kg to have an acceleration of 1 $\frac{m}{s^2}$

- <span style="color:green">- $\vec{F} = m\vec{a}$</span>

- <span style="color:blue">$\vec{a}$ or $\vec{p}$</span>, these have to be measured w.r.t. an <span style="color:blue">inertial frame</span> for newton's law to be valid.

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<footer style = "font-size: 18px">Newton's Second Law $\rightarrow$ Newton's Second Law $\rightarrow$ <span style = "color:blue"> Newton's Second Law </span> $\rightarrow$ Some Salient Points $\rightarrow$ Newton's Second Law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's Second Law </primary>
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- **b)**Newton second law is a vector law.

- <span style="color:green">- $\vec{F}, \vec{a}, \vec{p}$ are vectors.</span>

- $\vec{F}=m \vec{a}=\frac{d \vec{p}}{d t}$

- The scalar components of it is our first law.

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<footer style = "font-size: 18px">Newton's Second Law $\rightarrow$ Some Salient Points $\rightarrow$ <span style = "color:blue"> Newton's Second Law </span> $\rightarrow$ Newton's Second Law $\rightarrow$ Newton's Law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's Law </primary>
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- <span style="color:green">**c) Newton's Law:**</span> Valid for a point particle.

- The law can be extended for a finite body $\rightarrow$ <span style="color:green">Rigid body</span>

- i) Force $\rightarrow$ <span style="color:blue">External to the body</span>

- ii) <span style="color:blue">$\vec{a}$</span> $\rightarrow$ Acceleration of a special point = Centre of mass

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<footer style = "font-size: 18px">Newton's Second Law $\rightarrow$ Newton's Second Law $\rightarrow$ <span style = "color:blue"> Newton's Law </span> $\rightarrow$ Newton's Law $\rightarrow$ Impulse </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Impulse </primary>
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- a) $\vec{F}=\frac{d \vec{p}}{dt}$

- $\int^{t_2}_{t_1} \vec{F} d t=\int d\vec{p}$

- $\int^{t_2}_{t_1} \vec{F} d t $

- $ =\int_{\vec{p} \text{at} t=t_1}^{\vec{p} \text{at} t=t_2} d \vec{p}$

- $ = \vec{p_{t_2}} - \vec{p_{t_1}}$

- <span style="color:blue">Impulse</span>

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<footer style = "font-size: 18px">Newton's Law $\rightarrow$ Newton's Law $\rightarrow$ <span style = "color:blue"> Impulse </span> $\rightarrow$ Impulse $\rightarrow$ Newton's Third Law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Impulse </primary>
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- Impulse of a force acting on a particle from $t_1$ to $t_2$.

* Change in momentum of particle during this time interval.

- <span style="color:green"> $\vec{F}$ = Constant</span>

- $\int \vec{F} d t=\vec{F} \Delta t$

- $\vec{I}=\overrightarrow{F}_{\text {av. }} \Delta t$

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<footer style = "font-size: 18px">Newton's Law $\rightarrow$ Impulse $\rightarrow$ <span style = "color:blue"> Impulse </span> $\rightarrow$ Newton's Third Law $\rightarrow$ No Cause - Effect Relation </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's Third Law </primary>
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- When 2 bodies interact then $\vec{F_{AB}}$, force that body B exert on body A, is equal and opposite to $\vec{F_{AB}}$, when is the force that body A exerts on body B.

- To every action($\vec{F_{AB}}$) there is an equal and opposite reaction ($\vec{F_{AB}}$)

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<footer style = "font-size: 18px">Impulse $\rightarrow$ Impulse $\rightarrow$ <span style = "color:blue"> Newton's Third Law </span> $\rightarrow$ No Cause - Effect Relation $\rightarrow$ Newton's Third Law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
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* Action and reaction just imply mutual forces on interacting bodies gives a wrong impression that action is causing a reaction.

- <span style="color:green">In Newton's $3^{rd}$ Law</span>

- Mutual pair of force between bodies.

- Pair acts at the same time, so no cause effect relation.

- If we consider motion of A & B separately

- On body A, $\vec{F}_{AB}$ an extrenal force

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<footer style = "font-size: 18px">Impulse $\rightarrow$ Newton's Third Law $\rightarrow$ <span style = "color:blue"> No Cause - Effect Relation </span> $\rightarrow$ Newton's Third Law $\rightarrow$ Newton's Third Law </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Newton's Third Law </primary>
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* $\vec F_{AB}$ and  $\vec F_{BA}$ 
* They are equal and opposite and they act along the same line of action.
* $3_{rd}$ Law will be useful when we study system of particles

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<footer style = "font-size: 18px">No Cause - Effect Relation $\rightarrow$ Newton's Third Law $\rightarrow$ <span style = "color:blue"> Newton's Third Law </span> $\rightarrow$ Summary $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Laws Of Motion Newtons Second And Third Laws Of Motion L-6 </Success>
### <primary style="font-size:24px"> Summary </primary>
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- $I^{st}$ Law  $\rightarrow$ <span style="color:green">Statics</span>

- $II^{nd}$ Law  $\rightarrow$ <span style="color:green">$\vec{F}=m \vec{a}$</span>

- $III^{rd}$ Law  $\rightarrow$ <span style="color:blue">Mutually force between particle cancel out</span>

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<footer style = "font-size: 18px">Newton's Third Law $\rightarrow$ Newton's Third Law $\rightarrow$ <span style = "color:blue"> Summary </span> $\rightarrow$ Thank You $\rightarrow$  </footer>