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Questions and Answers
What is the rate of change of displacement?
What is the rate of change of displacement?
- Time
- Momentum
- Velocity (correct)
- Acceleration
Which of the following is a characteristic of an isolated thermodynamic system?
Which of the following is a characteristic of an isolated thermodynamic system?
- Matter is exchanged, but no energy is exchanged
- No energy or matter is exchanged with surroundings (correct)
- Energy is exchanged, but no matter is exchanged
- Energy and matter are exchanged with surroundings
What is the consequence of time dilation in special relativity?
What is the consequence of time dilation in special relativity?
- The speed of light appears to change for moving observers
- Time appears to pass slower for moving observers (correct)
- Time appears to pass faster for moving observers
- The length of objects appears to increase for moving observers
What is the result of applying a torque to an object in rotational motion?
What is the result of applying a torque to an object in rotational motion?
Which of the following is a consequence of the equivalence principle in general relativity?
Which of the following is a consequence of the equivalence principle in general relativity?
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Study Notes
Mechanics
Kinematics
- Study of motion without considering forces
- Key concepts:
- Displacement: shortest distance between initial and final positions
- Velocity: rate of change of displacement
- Acceleration: rate of change of velocity
- Time: scalar quantity measuring duration
- Frames of reference: inertial and non-inertial frames
Dynamics
- Study of motion considering forces
- Key concepts:
- Force: push or pull causing motion
- Newton's laws:
- First law (inertia): objects at rest stay at rest, objects in motion stay in motion
- Second law (F = ma): force equals mass times acceleration
- Third law (action and reaction): every action has an equal and opposite reaction
- Energy:
- Kinetic energy: energy of motion
- Potential energy: energy of position or configuration
- Momentum: product of mass and velocity
Rotational Motion
- Study of rotation around a fixed axis
- Key concepts:
- Angular displacement: angle of rotation
- Angular velocity: rate of change of angular displacement
- Angular acceleration: rate of change of angular velocity
- Torque: rotational force
- Rotational kinematics: analogs of linear kinematics for rotational motion
Thermodynamics
Laws of Thermodynamics
- Key concepts:
- Zeroth law: if two systems are in thermal equilibrium with a third, they are in thermal equilibrium with each other
- First law (energy conservation): energy cannot be created or destroyed, only converted
- Second law: total entropy of an isolated system always increases over time
- Third law: as temperature approaches absolute zero, entropy approaches a minimum value
Thermodynamic Systems
- Key concepts:
- Isolated systems: no energy or matter exchanged with surroundings
- Closed systems: energy exchanged, but no matter exchanged
- Open systems: energy and matter exchanged with surroundings
- Thermodynamic equilibrium: state of balance among system and surroundings
Thermodynamic Processes
- Key concepts:
- Isothermal: constant temperature
- Adiabatic: no heat exchanged
- Isobaric: constant pressure
- Isochoric: constant volume
- Cyclic processes: series of processes returning to initial state
Relativity
Special Relativity
- Key concepts:
- Time dilation: time appears to pass slower for moving observers
- Length contraction: objects appear shorter to moving observers
- Relativity of simultaneity: events simultaneous for one observer may not be for another
- Speed of light: always constant, regardless of observer motion
- Lorentz transformation: mathematical framework for relativity
General Relativity
- Key concepts:
- Gravitational time dilation: time passes slower near massive objects
- Gravitational redshift: light emitted from massive objects appears redder
- Equivalence principle: gravity and acceleration are equivalent
- Geodesic: shortest path in curved spacetime
- Einstein's field equations: mathematical description of gravity and spacetime curvature
Mechanics
Kinematics
- Displacement is the shortest distance between initial and final positions
- Velocity is the rate of change of displacement, measured in meters per second (m/s)
- Acceleration is the rate of change of velocity, measured in meters per second squared (m/s²)
- Time is a scalar quantity measuring duration, and is a fundamental concept in kinematics
- Frames of reference can be inertial (at rest or moving at a constant velocity) or non-inertial (accelerating)
Dynamics
- Force is a push or pull that causes motion, measured in Newtons (N)
- Newton's first law states that objects at rest stay at rest, and objects in motion stay in motion, unless acted upon by an external force
- Newton's second law states that force equals mass times acceleration (F = ma), and is a fundamental concept in dynamics
- Newton's third law states that every action has an equal and opposite reaction
- Energy has two main forms: kinetic energy (the energy of motion) and potential energy (the energy of position or configuration)
- Momentum is the product of mass and velocity, and is a measure of an object's tendency to keep moving
Rotational Motion
- Angular displacement is the angle of rotation, measured in radians (rad)
- Angular velocity is the rate of change of angular displacement, measured in radians per second (rad/s)
- Angular acceleration is the rate of change of angular velocity, measured in radians per second squared (rad/s²)
- Torque is a rotational force, measured in Newton-meters (N·m)
- Rotational kinematics has analogs of linear kinematics, including angular displacement, angular velocity, and angular acceleration
Thermodynamics
Laws of Thermodynamics
- The zeroth law states that if two systems are in thermal equilibrium with a third, they are in thermal equilibrium with each other
- The first law states that energy cannot be created or destroyed, only converted from one form to another
- The second law states that the total entropy of an isolated system always increases over time
- The third law states that as temperature approaches absolute zero, entropy approaches a minimum value
Thermodynamic Systems
- Isolated systems exchange neither energy nor matter with their surroundings
- Closed systems exchange energy, but not matter, with their surroundings
- Open systems exchange both energy and matter with their surroundings
- Thermodynamic equilibrium is a state of balance among the system and its surroundings
Thermodynamic Processes
- Isothermal processes occur at constant temperature
- Adiabatic processes occur without heat exchange
- Isobaric processes occur at constant pressure
- Isochoric processes occur at constant volume
- Cyclic processes are a series of processes that return to the initial state
Relativity
Special Relativity
- Time dilation occurs when time appears to pass slower for moving observers
- Length contraction occurs when objects appear shorter to moving observers
- Relativity of simultaneity states that events simultaneous for one observer may not be for another
- The speed of light is always constant, regardless of observer motion
- The Lorentz transformation is a mathematical framework for special relativity
General Relativity
- Gravitational time dilation occurs when time passes slower near massive objects
- Gravitational redshift occurs when light emitted from massive objects appears redder
- The equivalence principle states that gravity and acceleration are equivalent
- Geodesics are the shortest paths in curved spacetime
- Einstein's field equations provide a mathematical description of gravity and spacetime curvature
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