Projectile Motion

Basic Concepts

Projectile motion describes the motion of an object thrown or projected into the air, subject only to gravity. The path followed is typically a parabola.

• Key Equations:

• Horizontal position:

• Vertical position:

• Neglecting air resistance simplifies calculations.

• Initial velocity components: (horizontal), (vertical)

Example: A ball thrown horizontally from a cliff will follow a curved path due to gravity, landing some distance away from the base.

Conservation of Energy

Principle

The total energy in a closed system remains constant. Energy can change forms (kinetic, potential, thermal), but the sum is conserved.

• Key Equation:

• Applies to mechanical, thermal, and other energy forms.

Example: A pendulum at its highest point has maximum potential energy, which converts to kinetic energy as it swings down.

Conservation of Momentum

Linear and Angular Momentum

Momentum is conserved in isolated systems. There are two types: linear and angular.

• Linear momentum:

• Angular momentum:

• In collisions, total momentum before equals total momentum after.

Example: Two ice skaters push off each other and move in opposite directions, conserving momentum.

Torque

Definition and Formula

Torque is a measure of the rotational force applied to an object.

• Formula:

• Depends on the force applied and the distance from the axis of rotation.

Example: Opening a door by pushing at the edge creates more torque than pushing near the hinge.

Atoms and Phases of Matter

Atomic Structure and Matter

Atoms are the basic building blocks of matter, composed of protons, neutrons, and electrons. The arrangement and type of atoms determine the phase of matter (solid, liquid, gas).

• Electron energy levels (orbitals): Quantized due to attractive force between protons and electrons.

• Atomic number: Number of protons, determines element and energy levels.

Example: Water molecules (H2O) can exist as ice, liquid water, or steam depending on temperature.

Temperature, Heat, and Expansion

Thermal Concepts

Temperature measures the average kinetic energy of particles. Heat is energy transferred due to temperature difference. Expansion occurs when materials increase in size with temperature.

• Heat transfer equation:

• Q: Heat energy transferred

• m: Mass

• c: Specific heat capacity

• : Change in temperature

Example: Heating a metal rod causes it to expand in length.

Heat Transport

Modes of Heat Transfer

Heat can be transferred in three ways: conduction, convection, and radiation.

• Conduction: Transfer through direct contact (e.g., heating a pan).

• Convection: Transfer through fluid movement (e.g., boiling water).

• Radiation: Transfer through electromagnetic waves (e.g., sunlight).

Example: The Sun heats the Earth primarily by radiation.

Hooke's Law

Elasticity of Materials

Hooke's Law describes the relationship between the force applied to a spring and its extension.

• Formula:

• F: Restoring force

• k: Spring constant

• x: Displacement from equilibrium

Example: Stretching a spring twice as far requires twice the force.

Fluid Pressure

Definition

Fluid pressure is the force exerted by a fluid per unit area. It depends on the density of the fluid, gravity, and the height of the fluid column.

• Formula:

• P: Pressure

• : Density of fluid

• g: Acceleration due to gravity

• h: Height of fluid column

Example: Water pressure increases with depth in a swimming pool.

Buoyant Force

Archimedes' Principle

The buoyant force is the upward force exerted by a fluid on an object submerged in it. It equals the weight of the fluid displaced.

• Formula:

• Depends on: Density of fluid, gravity, and volume of object submerged.

Example: A boat floats because the buoyant force equals its weight.

Bernoulli's Principle

Fluid Dynamics

Bernoulli's Principle relates the pressure, velocity, and height in a moving fluid. It is a statement of energy conservation for flowing fluids.

• Equation:

• p: Pressure

• v: Fluid velocity

• h: Height

• : Fluid density

Example: Airplane wings generate lift due to pressure differences explained by Bernoulli's Principle.

Summary Table: Key Physics Equations

Additional info: Academic context and examples have been added to expand on brief notes and formulas, ensuring completeness and clarity for exam preparation.