Gravitation

Gravitation

1. Circular motion

   • Angular velocity is the angle an object rotates through in one second
   • angular velocity, w = angle / time
   • linear velocity, v = rw (r = radius of circle)
   • f = 1/T
   • For a complete turn an object rotates through 2π radians in a time T so w = 2πf
   • An object travelling in a circle is accelerating since its velocity is changing
   • Centripetal acceleration, a = w^2 r
   • Centripetal acceleration = v^2/r^2
   • The centripetal acceleration is produced by a centripetal force
     • F = mv^2/r
     • F = mw^2 r

2. Fields

   • masses in a gravitational field experience a force of attraction
   • Gravitational field lines show the direction of the force a mass would experience
   • Point masses have a radial field - spheres can be imagined as point masses with all the mass in the middle
   • Field strength
     • Is the force per unit mass
     • g = F/m
   • A mass in a uniform gravitational field experiences a constant force - eg near the earths surface field is uniform
   • ΔE(grav) = mgΔh
   • ΔGPE = ΔKE

3. Gravitational potential energy

   • In a radial field, g is inversely proportional to r^2
   • g decreases the further away you are from the mass
   • You gain GPE if you move away from the earth
   • The GPE at a certain point is the work that would be needed to move it from infinity to that point
   • G is a constant
   • • Work done against the force of gravity
   • GPE is potential energy per unit mass
     • Gravitational potential, V = GPE/m
     • E(grav) = GPE (CGP CONVERSION)

4. Orbits

   • Equipotentials
     • Equipotentials show all the points in a field which have the same potential
     • The surface of the earth is an equipotential
   • A satellite is any smaller mass that orbits a much bigger mass
   • How orbits work
     • 1) Earth feels a force due to the gravitational pull of the sun
     • 2) The earth has a velocity, v its linear speed is constant but direction is not so it is accelerating
     • 3) The centripetal force on the earth must be a result of the gravitational force due to the sun, and so the forces are equal

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