16/17, Circular Motion and Oscillations Flashcards
What is the equation for angular velocity?
ω = θ / t (angular velocity = change in angle / change in time) or ω = 2πf where f is frequency.
Equation for tangential velocity?
v = rω (speed = radius * angular velocity).
Equation for centripetal acceleration?
a = ω^2 r or a = v^2/r (acceleration = angular velocity squared * radius = speed squared / radius).
Equation for centripetal force?
F = ma = mω^2r = mv^2/r (centripetal force = mass * centripetal acceleration).
What experiment can find the relationship between radius, force and angular velocity?
Hang a mass through a tube (of a smooth material like glass) and spin an object at the other end, a marker can be used to control the radius and the weight of the mass is equal to the centripetal acceleration.
In oscillations what does the term displacement refer to?
The (+/-) distance from the equilibrium position.
In oscillations what does the term amplitude refer to?
The maximum displacement.
In oscillations what does the term period refer to?
The time taken for one full oscillation.
In oscillations what does the term frequency refer to?
The number of oscillations per unit time.
What defines simple harmonic motion?
a = -ω^2x (acceleration = -angular frequency squared * displacement, - sign shows acceleration returns the object to the equilibrium position).
What experiments can explore SHM?
Can use a spring with a mass on the end, pendulum or glider on air track for example, both can have masses, length of strings and starting amplitude as variables.
What shape is a displacement against time graph?
Sine/cosine graph.
How can the velocity and acceleration graphs be derived from the displacement graphs?
They are the first and second derivative (also giving a sinusoidal shape).
What equations would be used to give the displacement in SHM?
x = A cos ωt (or sine ωt) (displacement = Amplitude * cosine (angular frequency * time).
What is the maximum velocity of an oscillator and how is it derived?
From the equation v = +/- ω sqrt(A^2-x^2) it is obvious that a maximum occurs at x = 0 giving maximum velocity = ωA.
What types of energy can an oscillator have?
KE, GPE, elastic potential.
Characteristics of an oscillator with light damping?
Amplitude decreases slowly over time, frequency is almost unchanged (increases slightly).
What is a forced oscillation?
Where a periodic driving force is applied to an oscillator making it oscillate at the driving frequency.
What is resonance?
When the driving frequency is equal to the natural frequency of an object.
How is pendulums of different heights with one heavier pendulum at a height equal to one of the others all swinging off the same swing an example of resonance?
The pendulum at the same length will have the same natural frequency as the heavier pendulum so the heavier pendulum will drive the lighter one.
How quickly would a swinging pendulum with air resistance decay?
Exponentially, you get a sin(x) * e^-x type curve.
Examples of resonance being used?
MRI scanners, instruments are often made of a material which resonates with the notes.
What happens as you increase damping of a resonating object?
The amplitude at any driving frequency decreases, the maximum amplitude occurs at a lower frequency than the natural frequency and the peak of an amplitude against driving frequency graph gets flatter.
