Displacement, Speed, and Acceleration

Definitions and Key Concepts

• Displacement: The straight-line distance and direction from an object's initial to final position.

• Speed: The rate at which an object covers distance; instantaneous speed is the speed at a specific moment, while average speed is total distance divided by total time.

• Velocity: Speed with a specified direction.

• Acceleration: The rate of change of velocity with time.

• Mass: A measure of an object's inertia.

• Inertia: The tendency of an object to resist changes in its motion.

Vectors vs. Scalars

• Vector: A quantity with both magnitude and direction (e.g., velocity, force).

• Scalar: A quantity with only magnitude (e.g., mass, speed).

• Example: Displacement is a vector; distance is a scalar.

Motion Diagrams

• Used to represent speeding up, slowing down, and constant speed.

• Arrows indicate velocity; changing arrow length shows acceleration.

Circular Motion

• Motion along a circular path at constant or varying speed.

• Involves centripetal acceleration directed toward the center of the circle.

Newton's Laws of Motion

First Law (Law of Inertia)

• An object remains at rest or in uniform motion unless acted upon by a net external force.

Second Law

• The acceleration of an object is proportional to the net force and inversely proportional to its mass.

• Equation:

Third Law

• For every action, there is an equal and opposite reaction.

Law of Gravity

• Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

• Equation:

Forces and Equilibrium

• Net Force: The vector sum of all forces acting on an object.

• Equilibrium: When the net force is zero, resulting in no acceleration.

• Friction: A force that opposes motion between two surfaces.

Work and Energy

• Work: The product of force and displacement in the direction of the force.

• Equation:

• Kinetic Energy: Energy of motion,

• Potential Energy: Stored energy due to position,

Momentum

• Momentum: The product of mass and velocity,

• Impulse: Change in momentum,

• Conservation of Momentum: In a closed system, total momentum remains constant.

Rotational Motion

• Describes objects rotating about an axis.

• Angular Momentum: (where is moment of inertia, is angular velocity)

• Conservation of Angular Momentum: Total angular momentum remains constant if no external torque acts.

Gravity and Satellites

• Satellites orbit due to the balance between gravitational force and inertia.

• Orbital speed depends on the mass of the central body and the radius of the orbit.

Fluids, Pressure, and Buoyancy

• Density:

• Pressure:

• Buoyant Force: Upward force exerted by a fluid, equal to the weight of displaced fluid (Archimedes' Principle).

• Floating vs. Sinking: Depends on the relative densities of object and fluid.

Waves and Sound

• Wave: A disturbance that transfers energy through a medium or space.

• Frequency: Number of cycles per second (Hz).

• Speed of Sound: Depends on medium;

• Doppler Effect: Change in frequency due to relative motion of source and observer.

Energy Transformations and Conservation

• Energy can change forms (e.g., chemical to thermal, electrical to kinetic).

• Law of Conservation of Energy: Total energy remains constant in an isolated system.

Matter and Atomic Concepts

• Atoms consist of protons, neutrons, and electrons.

• Properties such as charge and location distinguish subatomic particles.

Summary Table: Key Physical Quantities

Additional info:

• Some topics (e.g., energy transformations, atomic structure) are summarized for completeness based on standard introductory physics curricula.