Circular Motion Concepts

Circular Motion

• Centripetal Force: The net force needed to keep an object moving in a circular path, directed toward the center.
• Centripetal Acceleration: The acceleration of an object moving in a circle, always directed toward the center.
• Radius (r): The distance from the center of the circular path to any point on its circumference.
• Angular Velocity (ω): The rate of change of angular displacement, measured in radians per second.
• Period (T): The time it takes for one complete revolution.
• Frequency (f): The number of complete revolutions per second.
• Angular Speed (ω): The rate at which an object rotates, calculated as angular displacement over time.
• Angular Displacement (θ): The angle through which an object rotates, measured in radians.
• Linear Speed (v): The rate at which an object moves along its circular path, related to angular speed by v = rω.
• Moment of Inertia (I): A measure of an object's resistance to changes in its rotational motion, dependent on mass distribution relative to the axis of rotation.
• Axis of Rotation: The line about which an object rotates.
• Rotational Inertia: The tendency of an object to resist angular acceleration.

Center of Mass

• Center of Mass: The point at which the total mass of a system is concentrated and balanced in all directions.
• Weighted Average Position: The center of mass is the weighted average of all particle positions in a system.

Torque

• Torque (τ): The measure of the rotational effect of a force applied to an object, dependent on the force, the lever arm, and the angle of application.
• Lever Arm (r): The perpendicular distance from the axis of rotation to the line of action of the force.

Gravitational Force

• Gravitational Force: The attractive force between two masses, governed by Newton's law of universal gravitation.
• Universal Gravitation Constant (G): A proportionality constant in the gravitational force equation.

Density and Pressure

• Density (ρ): The mass of an object per unit volume (ρ = m/V).
• Pressure (P): The force exerted per unit area (P = F/A).
• Hydrostatic Pressure: Pressure in a fluid at a given depth (P = ρgh).

Nature of Waves

• Wavelength (λ): The distance between two successive crests or troughs in a wave.
• Frequency (f): The number of wave cycles that pass a point per second.
• Amplitude: The maximum displacement of points on a wave from its equilibrium position.
• Wave Speed (v): The rate at which the wave propagates through a medium (v = λf).

Thermodynamics

• Heat (Q): The transfer of thermal energy due to temperature differences.
• Work (W): Energy transfer resulting from a force applied over a distance or from changes in volume in thermodynamic systems.
• Internal Energy (ΔU): The total energy contained within a system due to molecular motion and interactions.
• Entropy (S): A measure of the disorder or randomness of a system.
• Zeroth Law: Defines thermal equilibrium; if two systems are each in equilibrium with a third, they are in equilibrium with each other.
• First Law: Conservation of energy; the change in a system's internal energy is equal to heat added minus work done.
• Second Law: Entropy in an isolated system always increases, and heat flows naturally from hot to cold.
• Third Law: As a system approaches absolute zero, its entropy approaches a constant minimum.

Wave Motion

• Damped Harmonic Motion: Oscillators with non-conservative forces that dissipate their energy.
• Critical Damping: Returns the system to equilibrium as fast as possible without overshooting.
• Overdamping: An oscillator moves more slowly toward equilibrium than in critical damping.
• Underdamping: Causes the system to return to equilibrium with the amplitude gradually decreasing.
• Types of waves: Wave - a disturbance that travels or propagates from the place where it was created..
• Mechanical waves: require a medium to travel through
• Mechanical wave pulse: a sudden disturbance in which only one or a few waves are generated
• Mechanical wave periodic waves: repeats the same oscillation for several cycles
• Mechanical wave transverse wave: disturbance is perpendicular to the direction of propagation
• Mechanical wave longitudinal wave: is the disturbance is parallel to the direction of propagation
• Pulse: Described as a wave consisting of a single disturbance that moves through the medium.
• Periodic wave: Repeats the same oscillation.

Laws of Thermodynamics

• Zeroth Law: Defines thermal equilibrium.
• First Law: Conservation of energy.
• Second Law: Entropy increases in isolated systems.
• Third Law: Entropy approaches a constant minimum as a system approaches absolute zero.

Additional Concepts

• Archimedes' principle: When a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body
• Timbre: The musical quality of a tone resulting from the combination of harmonics.
• Beats: Periodic variations in amplitude.
• Principle of superposition: The principle of superposition for waves states that when multiple waves intersect, the resulting displacement is the sum of the individual waves' displacements.
• Standing waves: A wave pattern that doesn't appear to be moving in either direction, created when two waves with similar frequencies and amplitudes interfere.
• Nodes: Never moving points.
• Antinodes: Midway between nodes.
• Traveling wave: A wave that moves along the string.
• Doppler Effect: The frequency of a wave changes when the source or the observer is moving. Occurs when a source of sound and a listener are in motion relative to each other. The frequency of the sound heard by a listener changes, relative to the frequency of the source.