Further Mechanics Flashcards
What is angular speed?
The angle an object rotates through per second. ω = θ / t
What is frequency in circular motion?
Number of complete revolutions per second. f = 1 / T
What is time period in circular motion?
The time taken for one complete revolution. T = 1 / f
Where does the velocity of an object in circular motion act?
At a tangent to the circle.
Where does the centripetal acceleration of an object in circular motion act towards? How can it be calculated?
It’s directed to the center of the circle (always perpendicular to the velocity)
a = v2 / r = ω2r
In what direction does the centripetal force act and how can it be calculated?
The centripetal force acts towards the center of the circle. F = ma = mv2 / r = mω2r
What equation links an object in circular motion on a slop of angle θ, velocity v and a radius r?
tanθ = v2 / gr
What are the conditions for simple harmonic motion?
Displacement and acceleration are in opposite directions (a = -ω2x)
Displacement and acceleration are directly proportional to each other
How are frequency and time period defined in SHM?
Time period is the time taken for one cycle (a how long it takes for the object to get back to it’s starting position)
Frequency is the number of cycles per second
What do the frequency and time period of an oscillation not depend on in SHM?
The amplitude of the oscillation
Where does an object’s maximum acceleration occur at in SHM?
At the maximum magnitude of it’s displacement (where the displacement = amplitude)
amax = ± ω2A
What are the energy changes in SHM?
An object in SHM exchanges kinetic and potential energy as it oscillates.
For a spring it will be elastic potential energy and for a pendulum it will be gravitational potential energy.
Where is kinetic energy at a maximum in SHM?
At equilibrium position
Equilibrium position is where velocity is at its maximum
Ek = 1/2 mv2
Where is potential energy at its maximum in SHM?
At the maximum displacement (or where displacement = amplitude)
What is mechanical energy in SHM?
The sum of the potential and kinetic energy
It stays constant providing the motion isn’t damped
What are free vibrations?
They involve no transfer of energy to or from the surroundings
They have constant amplitude
They occur at the resonant/ natural frequency of the system
What are forced vibrations?
They happen when there is a periodic external driving force
This force has a frequency called the driving frequency (the frequency the system is forced to oscillate at)
What is resonance?
A phenomenon that can occur during forced vibrations
When the driving frequency approaches the resonant/ natural frequency, energy is gained from the driving force, amplitude increases
When the driving frequency = resonant frequency, resonance occurs and the maximum amplitude is reached
At resonance what is the the phase difference between the oscillator and the driver?
90 degrees (or π/2 radians) out of phase
When the driving frequency is lower than the natural frequency, what is the phase difference between the driver and the oscillator?
They are in phase
When the driving frequency is greater than the natural frequency, what is the phase difference between the driver and the oscillator?
They are in anti-phase (or 180 degrees or πradians out of phase)
What is damping?
When an oscillating systen loses energy to its surroundings due to frictional forces (called damping forces)
Systems can be damped to stop oscillations or minimise the effect of resonance
What does damping do?
It reduces the amplitude of the oscillation over time
This is because energy is directly proportional to the amplitude squared
vmax = ωA, Ek = 1/2 m(ωA)2
What is a lightly damped system?
These systems take a long time to stop oscillating
Their amplitude only reduces by a small amount each period
They have a sharp resonance peak (amplitude only increases dramatically when the driving force is very close to the natural frequency)
What is a heavily damped system?
These systems take less time to stop oscillating
Their amplitudes become much smaller each period
They have a broader resonance peak (they have less sensitivity to the driving, frequency)
Their resonanct frequency becomes slightly lower
What is critical damping?
It reduces the amplitude (stops the system from oscillating) in the shortest possible time
What is overdamping?
When the oscillations are stopped but it takes the system longer to return to equilibrium than a critical damped system.
