• Force
• Work
• Kinetic and Potential energy
• Conservation of energy

• Gravitation
• Electromagnetism
• Nuclear Forces
• Weak Interactions

• Galileo's Law
• Inertial and Gravitational Mass
• Equivalence

• 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

• Mass of the Earth
• Shape of the Earth

• Variation of $\mathrm{g}$
• Escape velocity
• Mass and weight

• Motion of the Moon

• Geostationary Orbits

Inertial Frame

No Force $\Longrightarrow$ No acceleration

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.

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.

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.

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.

Mass - Quantity of matter.

Independent of the state of motion.

Momentum: $\vec{p}=m \vec{v}$

Force: $\vec{F}_{a p p}=\frac{d \vec{p}}{d t}$

Mass : Quantity of Matter.

Not Volume.

Mass is independent of state of Motion.

$\vec{p}=m \vec{v}$

$\vec{F}_{\text {app }}=\frac {d \vec{p}}{dt}$

F applied is the cause and $\frac {d \vec{p}}{dt}$ is the effect.

Examples

Spring Mass system

Frictional Force

Velocity

Lorentz Force

Gravitation

$q \vec{E} + q (\vec{v} \times\vec{B})$

Force due to the electric field : $q \vec{E}$

Force due to the magnetic field : $q (\vec{v} \times\vec{B})$

The third law of Newton establishes a symmetry.

$\vec{F}_A{\rightarrow_B}$ = $-\vec{F}_B{\rightarrow_A}$

$\frac{d \vec{p}_1}{d t}+\frac{d \vec{p}_2}{d t}=0$

$F=-k x-k^{\prime} x^3 \ldots ...$

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, $\propto {v^2}$

$\vec{F}_A{\rightarrow_B}$ = $-\vec{F}_B{\rightarrow_A}$

$\frac{d \bar{p}_1}{d t}+\frac{d \vec{p}_2}{d t}=0$

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.

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.

$\vec{F}_A{\rightarrow_B}$ = $-\vec{F}_B{\rightarrow_A}$

$\vec{F}_A{\rightarrow_B}$ = $-\vec{F}_B{\rightarrow_A}$

$\frac{d \vec{p}_1}{d t}+\frac{d \vec{p}_2}{d t}=0$

The third law tells us, that the total momentum is a conserved quantity.