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Circular Motion, Projectile Motion, Motion and Gravitational Fields -…

- - - - Moving at a constant speed
    - - Linear Displacement
    - - Linear Velocity
      - Only valid for points on the edge of circle
        
        Points inside circle are different for both vel and disp
    - - No Constant Velocity
      - Average Velocity
        
        Displacement
        
        Period
  - - - faster it moves
        larger the acceleration
  - - - mass
      - Centripetal Acceleration
    - - always mass of moving object
  - - - Constant Frequency
      - Constant Time Period
- - - - Therefore, doesn't matter if disp and vel are different
  - - - Velocity
      - Length
    - - No energy change = no work done
        
        Radius Increase
        Velocity Increase
        
        Velocity Increase
        Kinetic Energy Increase
        
        Increase of Radius = Positive Work
        
        Decrease of Radius = Negative Work
- - - - Horizontal Components
        
        Vertical Components
        
        Normal Force
        
        non-zero net force
        
        Tension + Weight
        
        Newtons
    - - Frictional Force
        
        Reaction Force
        
        Parallel Reaction Force
        
        Perpendicular Reaction Force
        
        Net Force
    - - Net Force
        
        Limiting Friction
        
        Side Forces
        
        Limiting velocity without any sideways friction
        
        Closer angle is to 90 fast the limiting vel
        
        Angular Velocity
        
        Maximum Speed
  - - - In the Half-pipe
        
        Change in Kinetic Energy
        
        Negative change in Initial Velocity
        
        Net Force
        
        Normal Force
        
        Net force + W
        
        MUST be larger than net force
      - Amusing Circles
        
        Net Force
- - - - weight is equal and opposite to drag force
  - - - Decreases
        
        Horizontal range
        
        Vertical Range
  - - - Always zero without air resistance
    - - Always Constant
        
        -9.8ms^2
  - - - Proportional
        
        density of air which objects moves through
        
        Object's cross-section perpendicular to direction of motion
        
        Square of the object's speed
  - - - Find Magnitude
      - Find Direction
- - - - Ground Launch
        
        Final Velocity isn't involved
        
        Vertical Displacement = 0
    - - Horizontal Range
        
        Ground Launch
        
        distance
        
        Speed x Time
        
        x
    - - Time is not considered
        
        Final Vertical Velocity = 0
        
        Horizontal Acceleration always 0
  - - - Initial Vertical Velocity
        
        Vertical Displacement
        
        Quadratic Equation
      - Horizontal Launch
        
        Zero Initial Velocity
      - Initial Vertical Velocity
        
        Final Vertical Velocity
        
        Gravity
    - - Time of Flight
        
        Initial Horizontal Velocity
    - - Add Vertical Height
        
        Initial Vertical Velocity
        
        Vertical Velocity = 0
    - - Pythagoras Theorem
        
        Vertical Velocity
        
        SUVAT Equations
        
        Initial Horizontal Velocity = Final Horizontal Velocity
      - Degrees below the Horizontal
        
        Use cos θ = Adjacent/Hypotenuse
  - - - Assumptions
        
        Ignoring Air Resistance
        
        Overestimate Range
        
        Ignored Friction
        
        Overestimate Velocity
    - - Find Time
        
        SUVAT Equations
        
        Zero Final Velocity
        
        Vertical Displacement
        
        Zero Initial Horizontal Velocity
      - Identify Speed
        
        Potential Energy
        
        Change in PE =
        
        PE = KE
        
        Kinetic energy
        
        No Horizontal Acceleration
        
        Ball gains potential energy from top
        
        While rolling converts to kinetic energy
- - - - Upwards Throw
        
        Speed vs Time
        
        Velocity vs Time
        
        Acceleration vs Time
  - - - Initial vertical velocity
    - - acceleration is not negative
    - - No force = No acceleration
  - - - Only force acting on moving object
      - No Air Resistance
- - - - Eccentricity
        
        Eccentricity of Planets
        
        Mercury
        
        0.2056
        
        Venus
        
        0.0068
        
        Earth
        
        0.0167
        
        Mars
        
        0.0934
        
        Jupiter
        
        0.0483
        
        Saturn
        
        0.0560
        
        Uranus
        
        0.0461
        
        Neptune
        
        0.0097
        
        Degree of stretch
      - Ellipse Geometry
        
        Planet move in elliptical orbits
    - - Linear and angular speed is not constant
      - Areal speed is constant
      - Line joining sun to planet sweeps out equal areas in equal tiimes
    - - Square of period of any planet is proportional to the cube of the semi-major axis
        
        Constant for all planets round sun
        
        Mass and Period have an inverse square relationship
        
        Period SI
        
        Seconds
        
        Derived using centripetal and gravitational forces
  - - - Satellite
        
        satellite altitude + radius of the Earth
    - - Regularly repeating motion of objects in space around a large body
    - - Only considering
        
        The orbiting object
        
        What it's orbiting around
      - Orbit is following a circular path
    - - Orbital Velocity
        
        Mass of central body
        
        Orbital Radius
        
        Universal Gravitational COnstant
      - Orbital Period
        
        Increased Radius
        Increased Distance
        
        Increased Radius
        Decreased Speed
        
        Larger Radii = Longer Periods
  - - - Satellite remains just outside Earth's atmosphere throughout entire orbit
        
        Close to earth as possible while still being outside orbit
        
        Key Features
        
        Radius
        
        Velocity
        
        Period
        
        Key Uses
        
        Weather Monitoring
        
        Observing Earth
        
        Why
        
        Uses satellites to scan large portions of Earth
        
        Short period allows it to see more of Earth throughout orbit
        
        Orbital Decay
        
        When satellites in orbit slowly lose energy and spiral into Earth
        
        Small amount of air resistance slows satellite and causes decay
    - - Satellite maintains position directly above earth on a specific point
        
        Must be above point on equator so satellite can complete a full orbit
        
        Key Features
        
        Period
        
        Moves around Earth in the same time it takes to spin around
        
        Radius
        
        Velocity
        
        Key Uses
        
        Communications
        
        Satellite remains in fixed position
        
        Requires precise positioning to send/receive signals
        
        Geosynchronous
        
        A type of orbit with a period of 24 hours
        
        Doesn't have to orbit over equator
  - - - Low Earth = short
      - Geostationary = Long
    - - Low Earth = Small
      - Geostationary = Larger
    - - Low Earth = Fast
      - Geostationary = Slow
    - - Low Earth = True
  - - - Gravitational energy that can be stored in an object by moving it away from a large mass
    - - Universal Gravitational Constant
        
        Central Mass
        
        Object's Mass
        
        Distance from Object to mass' centre
      - When Radius = Infinity
        GPE = 0
        
        Any other position must be lower as you can't get further than infinity
        
        Therefore negative value
        
        Decreasing Radius = Negative Energy
  - - - Kinetic
        
        Object in orbit of radius
      - Potential
        
        GPE
  - - - The velocity needed to give an object so that it's able to fully escape the gravitational pull of a central mass
        
        When the object is so far away from central mass
        Gravity can never pull it back
    - - Independent of mass of the object that's trying to escape
        
        Mass decrease = Escape Velocity Decrease
- - - - Acceleration due to force is directly proportional to size of force
        
        Concludes
  - - - Region around a mass in which another mass experiences a gravitational force
        
        Force pulls objects towards earth
        
        Gravitational field lines point in direction of force
        
        Gravitational field strength
        
        How fast object accelerates within gravitational field
        
        Field around a point
        
        gravitational field strength
        
        Gravitational constant
        
        Distance from object's center
        
        further away the distance = larger the gravitational constant
        
        field strength inversely proportional to radius squared
        
        the greater the mass = greater field strength
        
        Mass of the point=like object
        
        larger mass = larger gravitational field strength
  - - - Dictates force experienced by a mass due to another mass
    - - Universal Gravitational Constant
        
        Finds Gravitational Force
        
        Masses
        
        Distance between masses