1. SMH and Circular motion Flashcards
Newtons 1st law
Every object will remain at rest or move with constant velocity unless acted upon by a resultant force
Centripetal acceleration
a = v² / r
Centripetal force
F = mv² / r
Angular velocity
The rate of change of angular displacement
Angular velocity eq
Change in angle / change in time
In RADIANS
When have rpm or other rotations per time
Revoultions x 2pi / (amount of seconds)
V also equals
V = wr
Centripetal force also equals
F = mw²r
At the top of the loop force equation
Force = Normal reaction + weight
At bottom of loop
Force = normal - weight
Simple harmonic motion examples
Guitar string
Pendulum
Car suspension
Conditions for SMH
The restoring force or acceleration acts towards the equilibrium
The magnitude of force or acceleration is proportional to the displacement
Conditons expressed as equations
Max acceleration
A = -w²x
Displacement SMH
X = A cos (wt +€)
What is phase constant? € ?
When the timing of the experiment starts which could mean the graph has shifted across on the axis
Velocity SMH
V = -Aw sin (wt + €)
Acceleration SMH
a = -w²A cos (wr + €)
Max kinetic energy SMH
½mw²A²
V max SMH
Vmax = Aw
amax SMH
a max = w²A
Mass spring systems
T = 2pi (m/k)^½
2 pi x square root of mass / spring constant
Simple pendulum
T = 2pi (l/g)^½
Resonance
When the frequency of the driving oscillator is equal to the natural frequency of the driven oscillator
What occurs at resonance?
Efficiency = Max
Amplitude = Max
Energy = Being transferred between driving and driven
When undergoing damping what is the shape of the graph and the type of slope
Envelope shape with exponential curve
Types of damping
Light
Critical
Over / heavy
When an object is in SMH what is happening with the energy
There is a constant transfer between PE and KE
What is a free oscialltion
When the oscillations arent effected by an external force
When would damping be used in real life
Car suspension to allow for a safer ride
Speedometers in car to ensure the speed can be read correctly without an oscillating needle
What happens in critical damping
The oscillations are quickly brought to rest
What will happen when you try to damp on resonance
The resonance curve on a graph will widen
