Glossary
Acceleration (in Inertial Reference Frames)
The rate of change of velocity of an object. A key principle is that the acceleration of an object remains constant and is measured the same in all inertial reference frames.
Example:
If a car brakes suddenly, its acceleration (deceleration) is the same whether measured by a passenger inside the car or by an observer standing on the sidewalk.
Acceleration (invariance in inertial frames)
The rate of change of velocity, which remains constant when measured from any inertial reference frame. Switching between inertial frames does not change the observed acceleration.
Example:
A ball thrown upwards on a moving train will still experience the same downward acceleration due to gravity (9.8 m/s²) as it would if thrown from the ground, because acceleration is invariant in inertial frames.
Conversion Between Reference Frames
The process of translating measurements (like velocity) from one reference frame to another, typically by accounting for the relative motion between the frames.
Example:
To find a bird's velocity relative to a moving car, you'd perform a conversion between reference frames by adding or subtracting the car's velocity from the bird's velocity relative to the ground.
Direction
The path or course along which something is moving or pointing, representing a component of a vector quantity.
Example:
A compass helps a hiker determine the direction of their trail, such as heading due north.
Direction (in Reference Frames)
The orientation of motion or a vector quantity as perceived from a specific reference frame. It can change depending on the observer's frame.
Example:
A ball thrown forward on a moving bus might appear to move straight ahead to a passenger, but its direction relative to someone outside the bus would be forward and also moving with the bus.
Inertial Reference Frame
A reference frame that is either at rest or moving with a constant velocity (not accelerating). Newton's laws of motion hold true in these frames.
Example:
A car cruising steadily on a straight highway at 60 mph is an inertial reference frame because it's not speeding up, slowing down, or turning.
Inertial Reference Frame
A reference frame that is either at rest or moving at a constant velocity, meaning it is not accelerating. In these frames, Newton's laws of motion hold true without the need for fictitious forces.
Example:
A spaceship drifting through deep space with its engines off is an excellent example of an inertial reference frame.
Magnitude
The size or extent of a physical quantity, representing its numerical value without regard to its direction.
Example:
The speedometer in a car shows the magnitude of its velocity, for instance, 60 mph, without indicating if it's going north or south.
Magnitude (in Reference Frames)
The numerical value or size of a vector quantity, such as speed or displacement, as measured from a particular reference frame. This value can vary between different frames.
Example:
If you walk at 1 m/s towards the front of a train moving at 20 m/s, your speed (magnitude) relative to the train is 1 m/s, but relative to the ground, it's 21 m/s.
Observed Velocity
The velocity of an object as measured by a specific observer from their particular reference frame. It is a combination of the object's motion and the observer's frame's motion.
Example:
If you're on a boat moving downstream, your observed velocity of a floating stick will be different than someone standing still on the riverbank.
Observed Velocity
The velocity of an object as measured by a specific observer from their particular reference frame, which can differ from the object's velocity relative to another frame.
Example:
If you are walking forward on a moving escalator, your observed velocity relative to someone standing still on the ground is the sum of your walking speed and the escalator's speed.
Reference Frame
A coordinate system or point of view from which motion is observed and measured. It defines the observer's perspective.
Example:
When you're on a moving train, the train itself is your reference frame, and you observe objects inside it differently than someone standing on the ground.
Reference Frame
A perspective or coordinate system from which an observer measures the direction and magnitude of physical quantities.
Example:
When you're sitting on a train, the train itself is your reference frame, and you perceive the trees outside as moving past you.
Relative Velocity
The velocity of an object or observer with respect to another object or observer, calculated using vector addition or subtraction of their individual velocities.
Example:
When two cars are driving towards each other, their relative velocity is the sum of their speeds, making them appear to approach each other very quickly.
Relative Velocity (in One Dimension)
The velocity of an object as measured from a moving reference frame, specifically when motion is restricted to a straight line. It is calculated by vectorially adding or subtracting velocities.
Example:
When two cars are driving towards each other on a straight road, their relative velocity is the sum of their individual speeds, indicating how quickly the distance between them is closing.
Vector Addition/Subtraction
Mathematical operations used to combine or find the difference between vector quantities, such as velocities, by considering both their magnitudes and directions.
Example:
To find the resultant velocity of a plane flying in a crosswind, you would use vector addition/subtraction to combine the plane's velocity relative to the air and the wind's velocity relative to the ground.