Periodic and Circular Motion Flashcards
What is Linear Velocity?
The rate of change of linear displacement
What is Angular Velocity?
The rate at which an object rotates relative to its axis of rotation.
What is the SI unit of angle?
Radians
What are the units and symbol of Angular Velocity?
Units: Rads^-1
Symbol: ω
How many radians are in a complete circle?
2π
What is the equation of Linear Velocity?
v = 2πr/T = 2πrf
What is the equation of Angular Velocity?
ω = 2π/T = 2πf = v/r
Whaich direction is acceleration in circular-motion?
Towards the axis of rotation
What is the equation for Centripetal Acceleration?
a = v²/r = ω²r
What is the equation for Centripetal Force?
F = mv²/r = mω²r
What direction is Centripetal Force acting in?
Towards the axis of rotation
Define Simple Harmonic Motion (SHM)?
It is a special type of circular-motion.
The acceleration is proportional to displacement and acts in the opposite direction.
Where is Dislpacement at its Maximum and Minimum?
Maximum: At Amplitude
Minimum: At Equilibrium
Where is Velocity at its Maximum and Minimum?
Maximum: At Equilibrium
Minimum: At Amplitude
Where is Accerleration at Maximum and Minimum?
Maximum: At Amplitude
Minimum: At Equilibrium
What is the equation for calculating the displacement at any time?
x = A Cos(ωt) = A Cos(2πft)
What are the units and symbol for Displacement?
Units: Meters (m)
Symbol: X
What are the units and symbol for Amplitude?
Units: Meters (m)
Symbol: A
What is the equation for acceleration at any time?
a = -ω²X = -(2πf)²X
What is the equation Maximum Acceleration?
a = ± ω²A = ±(2πf)²A
It is ± as it occurs on both side of equilibrium.
What is the equation for Velocity at any time?
v = ±ω(A²-X²)^0.5 = ±2π(A²-X²)^0.5
What is the equation for maximum Velocity?
v = ±ωA = ±2πfA
What is the equation for Total Energy of an SHM oscillator?
E=0.5mω²A²
What are two SHM oscillators?
Mass-Spring System
Simple Pendulum
What is the equation for the Period of a Mass-Spring System?
T = 2π(m/k)^0.5
What does the equation for the Period of a Mass-Spring System assume?
The spring obeys Hookes Law
The spring is not stretched beyond its elastic limit
What is the equation for the Period of a Simple Pendulum?
T = 2π(l/g)^0.5
What does the equation for the Period of a Mass-Spring System assume?
The pendulum is only displaced by a small angle
What is the equation for the Maximum Kinetic Energy of a SHM oscillator?
E = 0.5mω²A²
What is the equation for the Kinetic Energy at any point in an SHM oscillator?
E = 0.5mω²(A²-X²)
Where is Kinetic Energy at its Maximum and Minimum in and SHM oscillator?
Maximum: At Equilibrium
Minimum: At Amplitude
Where is Potential Energy at its Maximum and Minimum in and SHM oscillator?
Maximum: At Amplitude
Minimum: At Equilibrium
Where does Kinetic Energy and Potential Energy intercect on a Displacement-Energy graph?
At 0.5 E
As half the energy is kinetic and half is potential
What is a Damped Oscillator?
An Oscillator which loses energy to their surroundings.
What doesn’t change when an oscillator is damped?
The Period remains the same
what is thetotal energy of an oscillator proportional to?
The square of its displaement
X²
What is the defintion of an SHM oscillator?
a ∝ -x
What is meant by Free Oscillator?
An Oscillator with no damping
What is meant by Light Damping?
A system with (exponentially) decreasing amplitude
What is meant by Heavy damping
A system that takes a long time to reach the equilibrium position
What is meant by Critical Damping?
A system that reaches equilibrium and comes to rest in the shortest possible time ≈ t/2
What is an example of Light Damping?
Mass-Spring or Pendulum
Does the period change when an oscillator id lightly damped?
No
The period doesn’t change
What is an example of Heavy Damping?
Mass-Spring in a high viscosity fluid
Wha is an example of Critical Damping?
Car Suspension
Who desires Critical Damping and why?
Engineers
It limits vibration, as it returns to equilibrium then stops
Define Natural Frequency?
The frequency at which a system resonates when not subjected to an external force
What is the equation for the Natural frequency of a Mass-Spring System?
f=(1/2π)(k/m)^0.5
What is the equation for the Natural frequency of a Pendulum?
f=(1/2π)(g/l)^0.5
