Chapter 6.1: Further Mechanics Flashcards
What kind of force is required to keep an object moving in a circle at a constant speed?
A constant centripetal force. (Applied to the centre of a circle)
An object moving in a circle at a constant rate is accelerating. True of false?
True
What equation(s) can you use to calculate the magnitude of angular speed (ω)?
ω = v/r or ω = 2πf
ω - s^-1
What is angular acceleration in terms of angular velocity?
A = ω^2r
What is angular acceleration in terms of velocity?
a = v^2/r
What are the equations for centripetal force?
F=mv^2/r or F=mω^2r
What is a radian?
The angle of a circle sector such that the radius is equal to the arc length.
Radians are usually written in terms of π.
What are the conditions for SHM?
1) acceleration must be proportional to its displacement from the equilibrium point.
2) it must act towards the equilibrium point
3) a is proportional to -x
What is the constant of proportionality linking acceleration and x?
-ω^2 or -k/m
What is x as a trig function of t and ω?
x=Acos(ωt) or x=Asin(ωt)
How can you calculate the maximum speed using ω and A?
Max speed= ωA
How can you calculate the maximum acceleration using ω and A?
Max acceleration = ω^2A
What is the small angle approximation for sinx?
Sinx = x
Valid in radians
What is the small angle approximation for cosx?
Cosx = 1-x^2/2
Define free vibrations.
The frequency a system tends to vibrate at in a free vibration is called the natural frequency.
Define forced vibrations.
A driving force causes the system to vibrate at a different frequency.
Define damping and explain what is critical damping, overdamping and underdamping.
Damping occurs when an opposing force dissipates energy to the surroundings.
Critical damping reduces the amplitude to zero in the quickest time.
Overdamping is when the damping force is too strong and it returns to equilibrium slowly without oscillation.
Underdamping is when the damping force is too weak and it oscillates with exponentially decreasing amplitude.
What happens to a vibration with greater damping?
For a vibration with greater damping the amplitude is lower at all frequencies due to greater energy losses from the system. Resonant peak is broader.
What are some implications of resonance in real life?
Implications of resonance include that soldiers must break stop when crossing bridges and vehicles must be designed with no unwanted vibrations.
