### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> GRAVITATION </primary> <hr> <main> <div style='float: center;width:100%;font-size:100%'> </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px"> $\rightarrow$ $\rightarrow$ <span style = "color:blue"> GRAVITATION </span> $\rightarrow$ Outline of lectures $\rightarrow$ Outline Continued </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Outline of lectures </primary> <hr> <main> <div style='float: left; width:100%;font-size:25px;text-align:left'> - **Revision of concepts** - Force - Work - Kinetic and Potential energy - Conservation of energy - **Fundamental Forces** - Gravitation - Electromagnetism - Nuclear Forces - Weak Interactions </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px"> $\rightarrow$ GRAVITATION $\rightarrow$ <span style = "color:blue"> Outline of lectures </span> $\rightarrow$ Outline Continued $\rightarrow$ Outline continued II </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Outline Continued </primary> <hr> <main> <div style='float: left; width:100%;font-size:16px;text-align:left;max-width:450px;'> - **Freely falling body** - Galileo's Law - Inertial and Gravitational Mass - Equivalence - **Celestial Phenomena** - Determination of distances and periods - Kepler's Laws of planetary motion - Universal Law of Gravitation - Experimental determination of $G$ - Motion of the Moon around the Earth - Circular orbits and Kepler's Laws </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">GRAVITATION $\rightarrow$ Outline of lectures $\rightarrow$ <span style = "color:blue"> Outline Continued </span> $\rightarrow$ Outline continued II $\rightarrow$ Important Impact of Gravitation </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Outline continued II </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - **Basic Facts** - Mass of the Earth - Shape of the Earth - **Acceleration due to gravity** - Variation of $\mathrm{g}$ - Escape velocity - Mass and weight - **Satellite Motion** - Motion of the Moon - **Artificial Satellites** - Geostationary Orbits </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Outline of lectures $\rightarrow$ Outline Continued $\rightarrow$ <span style = "color:blue"> Outline continued II </span> $\rightarrow$ Important Impact of Gravitation $\rightarrow$ Review The Three Laws </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Important Impact of Gravitation </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - Terrestrial phenomena - Planetary system - Dynamics of stars - Galactic dynamics - Large scale structure of the universe </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Outline Continued $\rightarrow$ Outline continued II $\rightarrow$ <span style = "color:blue"> Important Impact of Gravitation </span> $\rightarrow$ Review The Three Laws $\rightarrow$ Review </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Review The Three Laws </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - Galiliean Law of inertia and inertial frame - Action of applied force - Action and Reaction: Conservation of momentum </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Outline continued II $\rightarrow$ Important Impact of Gravitation $\rightarrow$ <span style = "color:blue"> Review The Three Laws </span> $\rightarrow$ Review $\rightarrow$ The First Law Free Particles </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Review </primary> <hr> <main> <div style='float: left; width:50%;font-size:30px;text-align:left'> - Forces and Inertial Frames </div> <div style='float: right; width:50%;'> <!----> <img src='https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/198e6a4a-6c82-4e7e-aa04-a95480837500/public'/> </div> </main> <hr> <footer style = "font-size: 18px">Important Impact of Gravitation $\rightarrow$ Review The Three Laws $\rightarrow$ <span style = "color:blue"> Review </span> $\rightarrow$ The First Law Free Particles $\rightarrow$ Motion of a Body </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> The First Law Free Particles </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - **Inertial Frame** - No Force $\Longrightarrow$ No acceleration </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Review The Three Laws $\rightarrow$ Review $\rightarrow$ <span style = "color:blue"> The First Law Free Particles </span> $\rightarrow$ Motion of a Body $\rightarrow$ State of Motion </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Motion of a Body </primary> <hr> <main> <div style='float: left; width:60%;font-size:30px;text-align:left'> - Assume body is a point particle. - **Kinematic Relativity** - If B is moving with a velocity v with respect to A, then from the view point of B, A is moving with a velocity -v. </div> <div style='float: right; width:40%;'> <img src='https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/c4872335-b5b1-4878-20f4-6856b1c95d00/public'/> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Review $\rightarrow$ The First Law Free Particles $\rightarrow$ <span style = "color:blue"> Motion of a Body </span> $\rightarrow$ State of Motion $\rightarrow$ Merry Go Round </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> State of Motion </primary> <hr> <main> <div style='float: left; width:50%;text-align:left;font-size:30px;'> - Change of state of motion of a body requires force. </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/875b3161-8c5b-4050-b362-9ecae53a9a00/public" style= 'width:500' > </div> <div style='float: right; width:0%;'> <!----> <!----> </div> </main> <hr> <footer style = "font-size: 18px">The First Law Free Particles $\rightarrow$ Motion of a Body $\rightarrow$ <span style = "color:blue"> State of Motion </span> $\rightarrow$ Merry Go Round $\rightarrow$ Fixed Stars </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Merry Go Round </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - In a merry-go-round, you are going round about the central pole, but if you look around, it would appear as if the rest of the world rotates. - $ a=\frac{v^2}{r}$ - The change of motion caused by the force can be properly described only in some frames. </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Motion of a Body $\rightarrow$ State of Motion $\rightarrow$ <span style = "color:blue"> Merry Go Round </span> $\rightarrow$ Fixed Stars $\rightarrow$ Galileo </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Fixed Stars </primary> <hr> <main> <div style='float: left; width:70%;font-size:30px;text-align:left'> - The stars are fixed, the earth is rotating about its axis. </div> <div style='float: right; width:30%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/7bc0523c-1728-487f-d846-804422e62100/public" style='width:80%'> </div> <div style='float: right; width:0%;'> <!----> <!----> </div> </main> <hr> <footer style = "font-size: 18px">State of Motion $\rightarrow$ Merry Go Round $\rightarrow$ <span style = "color:blue"> Fixed Stars </span> $\rightarrow$ Galileo $\rightarrow$ Inertial Frames </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Galileo </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - We assume that we know how to distinguish free particles from others. - Once we isolate these free particles, it has nothing to do with their state of motion. - Identify special Frames of Reference. - The concept of frame of reference are called inertial. </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Merry Go Round $\rightarrow$ Fixed Stars $\rightarrow$ <span style = "color:blue"> Galileo </span> $\rightarrow$ Inertial Frames $\rightarrow$ Second Law </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Inertial Frames </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - Inertial frames of references are those frames in which a body is not acted upon by any force will not accelerate. - No acceleration $\Longleftrightarrow$ No Force. - Experiment: Foucault pendulum. - Uniform Velocity: Magnitude and Direction. </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Fixed Stars $\rightarrow$ Galileo $\rightarrow$ <span style = "color:blue"> Inertial Frames </span> $\rightarrow$ Second Law $\rightarrow$ Second Law </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Second Law </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - Mass - Quantity of matter. - Independent of the state of motion. - Momentum: $\vec{p}=m \vec{v}$ - Force: $\vec{F}_{a p p}=\frac{d \vec{p}}{d t}$ </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Galileo $\rightarrow$ Inertial Frames $\rightarrow$ <span style = "color:blue"> Second Law </span> $\rightarrow$ Second Law $\rightarrow$ Momentum </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Second Law </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - **Mass :** Quantity of Matter. - Not Volume. - Mass is independent of state of Motion. </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Inertial Frames $\rightarrow$ Second Law $\rightarrow$ <span style = "color:blue"> Second Law </span> $\rightarrow$ Momentum $\rightarrow$ Force </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Momentum </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - $ \vec{p}=m \vec{v} $ - $ \vec{F}_{\text {app }}=\frac {d \vec{p}}{dt} $ - F applied is the cause and $\frac {d \vec{p}}{dt}$ is the effect. </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Second Law $\rightarrow$ Second Law $\rightarrow$ <span style = "color:blue"> Momentum </span> $\rightarrow$ Force $\rightarrow$ Lorentz Force </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Force </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - <b>Examples</b> - Spring Mass system - Frictional Force - Velocity - Lorentz Force - Gravitation </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Second Law $\rightarrow$ Momentum $\rightarrow$ <span style = "color:blue"> Force </span> $\rightarrow$ Lorentz Force $\rightarrow$ Third Law Conservation of Momentum </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Lorentz Force </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - $ q \vec{E} + q (\vec{v} \times\vec{B})$ - Force due to the electric field : $q \vec{E}$ - Force due to the magnetic field : $q (\vec{v} \times\vec{B})$ </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Momentum $\rightarrow$ Force $\rightarrow$ <span style = "color:blue"> Lorentz Force </span> $\rightarrow$ Third Law Conservation of Momentum $\rightarrow$ Spring Mass System </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Third Law Conservation of Momentum </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - The third law of Newton establishes a symmetry. - $\vec{F}_A{\rightarrow_B}$ = $-\vec{F}_B{\rightarrow_A}$ - $\frac{d \vec{p}_1}{d t}+\frac{d \vec{p}_2}{d t}=0$ </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Force $\rightarrow$ Lorentz Force $\rightarrow$ <span style = "color:blue"> Third Law Conservation of Momentum </span> $\rightarrow$ Spring Mass System $\rightarrow$ Third Law Conservation of Momentum </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Spring Mass System </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - $F=-k x-k^{\prime} x^3 \ldots ...$ - F = -kx, is valid only for small displacements. - Viscosity or friction, it can be constant for small velocities. - a block moving on a rough surface, $\propto {v}$ - At very large speeds, $\propto {v^2}$ </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Lorentz Force $\rightarrow$ Third Law Conservation of Momentum $\rightarrow$ <span style = "color:blue"> Spring Mass System </span> $\rightarrow$ Third Law Conservation of Momentum $\rightarrow$ Second Law </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Third Law Conservation of Momentum </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - $\vec{F}_A{\rightarrow_B}$ = $-\vec{F}_B{\rightarrow_A}$ - $\frac{d \bar{p}_1}{d t}+\frac{d \vec{p}_2}{d t}=0$ </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Third Law Conservation of Momentum $\rightarrow$ Spring Mass System $\rightarrow$ <span style = "color:blue"> Third Law Conservation of Momentum </span> $\rightarrow$ Second Law $\rightarrow$ Second Law </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Second Law </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - In second law, there is an asymmetry. - $\vec{F}_{a p p}=\frac{d \vec{p}}{d t}$ - Earth is causing the ball to move. </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Spring Mass System $\rightarrow$ Third Law Conservation of Momentum $\rightarrow$ <span style = "color:blue"> Second Law </span> $\rightarrow$ Second Law $\rightarrow$ Third Law Conservation of Momentum </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Second Law </primary> <hr> <main> <div style='float:left;width:100%;font-size:30px;text-agn:left'> - Remember velocity, momentum, acceleration, force, angular momentum, they are all vectors. - The change of momentum of B is because of the action of A. The change of momentum of A is because of the action of B on A. - $\vec{F}_A{\rightarrow_B}$ = $-\vec{F}_B{\rightarrow_A}$ </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Third Law Conservation of Momentum $\rightarrow$ Second Law $\rightarrow$ <span style = "color:blue"> Second Law </span> $\rightarrow$ Third Law Conservation of Momentum $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Third Law Conservation of Momentum </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px;text-align:left'> - $\vec{F}_A{\rightarrow_B}$ = $-\vec{F}_B{\rightarrow_A}$ - $\frac{d \vec{p}_1}{d t}+\frac{d \vec{p}_2}{d t}=0$ - The third law tells us, that <span style="color:blue">the total momentum is a conserved quantity</span>. </div> <div style='float: right; width:0%;'> <!----> </div> </main> <hr> <footer style = "font-size: 18px">Second Law $\rightarrow$ Second Law $\rightarrow$ <span style = "color:blue"> Third Law Conservation of Momentum </span> $\rightarrow$ Thank You $\rightarrow$ </footer>

### <Success style="font-size:25px"> Gravitation L-5 </Success> ### <primary style="font-size:24px"> Thank You </primary> <hr> <main> <div style='float: left; width:100%;font-size:30px:text-align:left;'> </div> <div style='float: right; width:0%;'> <!----> </main> <hr> <footer style = "font-size: 18px">Second Law $\rightarrow$ Third Law Conservation of Momentum $\rightarrow$ <span style = "color:blue"> Thank You </span> $\rightarrow$ $\rightarrow$ </footer>