Physics, Conservation laws, & Oscillations Flashcards
Rate of change
How much a quantity will change in a given amount of time
Velocity
The rate of change of an object in a certain direction
Speed
The velocity in the direction of motion
- always positive
change in position = velocity x (elapsed time)
Newton’s first law
The velocity in each direction is constant in the absence of interactions
-ie, objects move at a constant speed in a fixed direction
Conserved quantities
Quantitative properties of a physical system that remain constant in time
- energy
- momentum
- spin
Mass
The energy of an object at rest
Kinetic energy
The energy that an object has due to its motion
Momentum
Energy carried by a moving object in the direction it is moving
momentum = mass x velocity
Quantifies how hard it is to stop the object’s movement
If objects interact,
the sum of the momenta before = the sum of the momenta after
An equal strength push on two different objects will lead to the same change in momentum
Spin (angular momentum)
Related to mass, size, and period of rotation
Conservation of angular momentum: an isolated spherical object of fixed size will spin with a fixed period or rotation about a fixed axis
Force
Quantifies the instantaneous strength of a push or pull
Force = rate of change of momentum (in absence of other forces)
Newton’s second law
A force of 1 Newton will cause a 1kg object to change its velocity by 1 m/s in 1 second
1 Newton = 1 kg m/s /s
Force of gravity
A downward force with magnitude
F = M x g
M = mass; g = 9.8 m/s /s
Rules for predicting positions and velocities
Newton’s third law
When there is a force from object A on object B, there should be an equal opposing force from object B on object A
(equal in strength, opposite in direction)
Mechanical equilibrium
An object is in mechanical equilibrium if it is at rest and the net force on the object is zero
Restoring forces
An object displaced from equilibrium in one direction experiences a net force in the other direction, leading to oscillations
Hooke’s law
Restoring force is proportional to the displacement of the object (eg. doubling displacement doubles force)
F = -k x
x: displacement
k: constant (depends on the specific system)
Oscillations caused by Hooke’s law obey simple harmonic motion and the period/frequency is independent of the amplitude
Simple harmonic motion
Oscillations have sinusoidal time graphs (sine waves)
Amplitude
The maximum distance that an object is displaced from equilibrium during an oscillation
Determined by initial displacement and/or initial velocity
Frequency
Decreases as mass of the oscillator increases (eg, stiffer string)
Increases as strength of restoring forces increases (eg, tension)
Potential energy
Energy associated with the configuration of an object (eg, how much a spring is stretched)
Heat
The kinetic energy associated with the random motions of molecules in a material
What is the relationship between energy and oscillations?
In an oscillation, energy is transferred back and forth between kinetic and potential energy
In an oscillation, energy is proportional to the square of amplitude (eg, if the amplitude is multiplied or divided by 3, the energy is multiplied or divided by 9)
Driven oscillation
An oscillation sustained by a periodic force acting on the oscillator
Resonance
The amplitude of a driven oscillation becomes large when the frequency of the driving force matches the natural frequency of the oscillator
Natural frequency
In the absence of a driving force, the frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed
