Circular motion and SHM summary notes

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Circular motion
A free body following a circular path is said to be undergoing circular motion.
whilst the body may have a constant speed its
velocity is always changing because it changes direction
towards the centre of the circle.
it has centripetal acceleration
A=acceleration
v=velocity
r=radius
Radians
a radian is an angle the angle you get if you draw an arc that has the same length as the
radius
in 180 there are just over 3 radians because 180 =
Angular velocity
Angular displacementthis tells you the angle "swept out" by an object undergoing circular
motion
angular velocity this tells you the angle that is swept out by an object in a certain period
Equations
v=w x r
A=w^2 x r
F=mw^2 x r
F=w^2/r

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Oscillating springs
a mass spring system will always oscillate with simple harmonic motion of period:
mass can be replaced by
length and k by gravity
therefore the only two factors that affect the period of a spring are
1. The mass
2. The spring constant
Amplitude has no effect because greater amplitude means greater distance to
cover but also greater restoring force.
Acceleration and maximum velocity the effects cancel out and do not affect the
period.…read more

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Acceleration and displacement are
equal but in opposite directions.
Velocity is the odd one out it is ½ way
between the two.
The restoring force is proportional to displacement but in the opposite direction
Velocitymax=Aw
Velocity=Awsin(wt)
Accelerationmax=w2A
Acceleration=w2r
Acceleration=w2Acos(wt)
Energy and Simple Harmonic Motion
This graph shows the energy of a
spring undergoing simple harmonic motion.…read more

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This is assuming there are no forces working against it such as gravity and air
resistance.
To calculate the maximum potential energy E=1/2KX2 remember that x will be A at
maximum x)
to work out over time. energy=½ k(acos(wt))2
For kinetic energy =½ mv(Awsin(wt))2
Resonance
If a system is undergoing simple harmonic motion and allowed to oscillate freely, it will
oscillate at it's natural frequency.
A system can be made to oscillate by a periodic driving force.…read more

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