Gravitational Field Intensity (I): Force per unit mass. $I = \frac{GM}{r^2}$.

Gravitational Potential (V): Potential energy per unit mass. $V = -\frac{GM}{r}$.

Gravitational Potential Energy (U): $U = -\frac{Gm_1m_2}{r}$.

Escape Velocity ($v_e$): Minimum velocity to escape gravitational field. $v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}$.

Orbital Velocity ($v_o$): Velocity for circular orbit. $v_o = \sqrt{\frac{GM}{r}}$. Relation: $v_e = \sqrt{2}v_o$.

Time Period of Satellite: $T = 2\pi\sqrt{\frac{r^3}{GM}}$.

Kepler's Laws:

1st Law (Orbits): Planets move in ellipses with Sun at one focus.
2nd Law (Areas): Line joining Sun to planet sweeps equal areas in equal times. (Conservation of Angular Momentum)
3rd Law (Periods): $T^2 \propto r^3$ (r: semi-major axis).

Weightlessness: When apparent weight is zero (e.g., free fall, orbiting satellite).

Elasticity: Property of material to regain original shape after deforming force removal.
Stress ($\sigma$): Restoring force per unit area. $\sigma = \frac{F}{A}$. Unit: $N/m^2$ (Pascal).
- Longitudinal (Tensile/Compressive), Shearing (Tangential), Volumetric.
Strain ($\epsilon$): Ratio of change in configuration to original configuration. Dimensionless.
- Longitudinal ($\frac{\Delta L}{L}$), Shearing ($\phi = \frac{\Delta x}{L}$), Volumetric ($\frac{\Delta V}{V}$).
Hooke's Law: Stress $\propto$ Strain. $\sigma = E\epsilon$. (E: Modulus of Elasticity)
- Young's Modulus (Y): $\frac{\text{Longitudinal Stress}}{\text{Longitudinal Strain}}$.
- Shear Modulus (G): $\frac{\text{Shearing Stress}}{\text{Shearing Strain}}$.
- Bulk Modulus (B): $\frac{\text{Volumetric Stress}}{\text{Volumetric Strain}}$. Compressibility: $C = \frac{1}{B}$.
Poisson's Ratio ($\nu$): $\frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}$.
Work Done in Stretching a Wire: $W = \frac{1}{2} \text{Stress} \times \text{Strain} \times \text{Volume} = \frac{1}{2} \frac{Y(\Delta L)^2}{L} A$.

Fluids: Substances that flow (liquids, gases).
Pressure (P): Force per unit area. $P = \frac{F}{A}$. Unit: Pascal (Pa).
- Atmospheric Pressure: $P_{atm} \approx 1.01 \times 10^5 \text{ Pa}$.
- Hydrostatic Pressure: $P = P_0 + \rho gh$. (P increases with depth).
- Gauge Pressure: $P_{gauge} = P - P_{atm} = \rho gh$.
Pascal's Law: Pressure applied to enclosed fluid is transmitted undiminished to every portion of fluid and walls.
Archimedes' Principle (Buoyancy): $F_B = V_{displaced} \rho_{fluid} g$.
- Apparent Weight: $W_{app} = W_{actual} - F_B$.
- Floatation: If $\rho_{body} < \rho_{fluid}$, object floats. If $\rho_{body} > \rho_{fluid}$, object sinks.
Types of Flow:
- Steady Flow: Velocity, pressure, density constant at a point over time.
- Streamline Flow: Particles follow same path as preceding particle.
- Laminar Flow: Fluid moves in parallel layers.
- Turbulent Flow: Irregular, disordered motion (above critical velocity).
Equation of Continuity: $A_1v_1 = A_2v_2 = \text{constant}$ (for incompressible fluid).
Bernoulli's