2922338
Description
Mind Map by Harry Archer, updated more than 1 year ago
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Created by Harry Archer
almost 9 years ago
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Circular Motion + Ocillations
- Circular Motion
- Angular Speed
- Angle an object rotates through per second
- ω = θ/t
- Linked to linear speed
- v = rω
- v = rω
- Angle an object rotates through per second
- Fequencey and Period
- ω = 2πf
- ω = 2π/T
- ω = 2πf
- Objects travelling in circles
are accelerating since their
velocity is always changing
- a = v^2/r
- a = ω^2r
- Created by a centripetal force acting
towards the center of the circle
- F = mv^2/r
- F = mω^2r
- F = mv^2/r
- a = v^2/r
- Angular Speed
- Gravitational Fields
- Motion of Masses
- v = √GM/r
- T = 2πr/v
- Substitute for v
- T^2 = (4π^2/GM)r^3
- T^2 = (4π^2/GM)r^3
- Substitute for v
- T = 2πr/v
- Geostationary satellites have the
same angular speed as the earth turns
below it
- Kepler's 3rd Law
- T^2 ∝ r^3
- T^2 ∝ r^3
- v = √GM/r
- An object with mass will experience an attractive force
when placed in the gravitational field of another object
- Newton's Law of Gravitation
- F = -GMm/r^2
- r = distance between
center points
- r = distance between
center points
- This is an inverse square law
- F ∝ 1/r^2
- F ∝ 1/r^2
- F = -GMm/r^2
- Gravitational field strength
- Force per unit mass
- g = F/m
- g = -GM/r^2
- Inverse square law applies
- Inverse square law applies
- g = -GM/r^2
- Force per unit mass
- Motion of Masses
- Simple Harmonic Motion
- An object in SHM oscillates either side of a midpoint
- There is always a restoring force pushing the object back to the midpoint
- Restoring force exchanges PE and KE
- PE -> KE towards midpoint as restoring force does work
- PE -> KE towards midpoint as restoring force does work
- Restoring force exchanges PE and KE
- There is always a restoring force pushing the object back to the midpoint
- Velocity
- Vmax = (2πf)A
- Vmax = (2πf)A
- Acceleration
- amax = -(2πf)^2A
- amax = -(2πf)^2A
- Displacement
- Start at midpoint = Sin
- Start at amplitude = Cos
- Start at midpoint = Sin
- An object in SHM oscillates either side of a midpoint
- Free and Forced Vibrations
- Free
- No transfer of energy with surroundings
- Keeps oscillating with the same amplitude
forever
- No transfer of energy with surroundings
- Forced
- External driving force present
- Frequency of the force = Driving frequency
- Frequency of the force = Driving frequency
- External driving force present
- Resonance
- When Driving force = Natural Frequency
- Damping
- Reduces amplitude of
oscillation over time
- Critical Damping
- Reduces amplitude in the shortest
time possible
- Reduces amplitude in the shortest
time possible
- Overdamping takes longer to return to
equilibrium than critical
- Decreases amplitude
of resonance
- Reduces amplitude of
oscillation over time
- When Driving force = Natural Frequency
- Free
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