Circular Motion & Gravity

Circular Motion & Gravity

1. Linear velocity

   • v=2πr/T
     • • v= linear velocity (ms) • r= radius of rotation • T= period (time for one full rotation)

2. Angular velocity

   • ω=θ/T
     • ω=2π/T (In one complete revolution as θ=2π
       • v=rω
     • ω- Angular velocity (rads-1/ms) θ- Angle through which object turns (in radians) T− time taken to turn through θ

3. Centripetal Acceleration

   • Consider an object moving at a CONSTANT speed in a circle: Although speed is constant, velocity is changing= acceleration
   • ALWAYS ACTS TOWARDS THE CENTRE OF A CIRCLE
   • a=v^2/r
     • a- centripetal acceleration (ms^2) v^2- linear speed (ms) r- radius of momentum (m)

4. Centripetal Force

   • Any object moving in a circular path has a centripetal acceleration which is provided by a centripetal FORCE, acting towards the centre
   • Using F=ma
     • F=(mv^2)/r
       • Where v= linear velocity
   • Weightlessness on the ISS
     • Astronauts feel 'weightless' as they have the same acceleration as the ISS. They only feel forces applied by contact with the walls of the ISS. However they have no support force from the station as they have the acceleration as the ISS

5. Gravitational Field

   • Field: a region in which a force is ecerted on an object at a distance
   • Produced by any mass and affects
   • Gravitational field strength (g)= force per unit mass
     • Vector- the direction in which a mass would feel a force
       • Represented by field lines
   • Gravitational Field Lines
     • 1. Start at infinity and end on a mass
       • 2. Act as though they terminate at the centre of a mass
         • 3. Always perpendicular to the surface of a spherical mass
           • 4. Field lines never cross
             • 5. Field line density is proportional to field strength
               • 6. Don#t really exist!

6. Newton's Laws of Graviation

   • Gravitational fields are radial -> obey an inverse square law
   • Newton experimented with masses he varied: -size of the masses -distance between their centres
   • F ∝ m F ∝ M F ∝ 1/d^2

7. Kepler

   • First Law: All planets follow elliptical orbits
     • Third Law: The square of the period of a planet is directly proportional to the cube of its orbital radius
       • Derivation- Assume the orbital path is circular, not elliptical.

8. Satellites

   • An object that orbits a planet
   • Natural satellites, e.g. Moon
   • Aritifical Satellites, e.g Hubble Space Telescope
     • 2 types: Geostationary and Low-Orbit (polar)
       • Geostationary- must have a period of 24 hours and stay in the same position above the Earth's equator, e.g. GPS & communication satellites
       • Low Polar Orbits- passes above both poles at low altitudes, e.g. Spy & Weather satellites

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