Lecture 5 Dynamics of Uniform Circular Motion by nml23533


									            Lecture 5:
Dynamics of Uniform Circular Motion
                     Uniform Circular Motion
Uniform circular motion is the motion of an object traveling at a constant (uniform) speed
on a circular path.

                                               Period, T = Time required to travel once
                                               around the circle or complete one

  In UNIFORM circular motion, the “speed”- magnitude of the velocity vector is a
  But the direction is NOT A CONSTANT
              Centripital Acceleration
•“Centripital” – Center Seeking
• Since the velocity vector under uniform circular motion
changes, there must be an acceleration – CENTRIPITAL
acceleration (ac) .
• Magnitude of ac depends on the speed of the object (v) and
the radius (r) of the circular path.
• Magnitude: The centripetal acceleration of an object moving
with a speed v on a circular path of radius r has a magnitude
ac given by : v2/r
• Direction: The centripetal acceleration vector always points
toward the center of the circle and continually changes
direction as the object moves
                         Centripital Force
  •Newton’s Second Law: F = ma, when ever there
  is an acceleration, there should be a net force
  associated with that.
  • CENTRIPITAL Force: (Fc) points in the same
  direction as the centripital acceleration – towards
  the center of the circle.

Magnitude: The centripetal force is the name given to the net force required to
keep an object of mass m, moving at a speed v, on a circular path of radius r,
and it has a magnitude of

Direction: The centripetal force always points toward the center of the circle
and continually changes direction as the object moves.
Centripital Force – Is this a “NEW” Force?
•Does NOT denote a New and Separate force created by nature
•It is the net force pointing towards the center of the circular path
•This net force is the vector sum of all force components that point in the
radial direction
           Banked Curves

               mv 2
FC  FN Sin 
FN Cos  mg

       No Need of friction to hold the car in place
                 Satellites in Circular Orbit
• Gravitational force( pull) provides the
centripital force
• There is only one speed that the satellite can
have if it is to remain in an orbit of fixed radius.

        GM E ms mv 2
   FC      2
          r      r
        GM E
• Closer the satellite, the greater nee\\ds to be
the velocity.
• Note: Mass, ms of the satellite does not appear
in the equation => for a given orbit a satellite
with large mass has exactly the same orbital
speed as a satellite with small mass.
Global Positioning Satellites
- 24 Satellites
- Each satellite has an atomic clock (Remember the need for precision timing)
- Cars with GPS receive radio signals from these satellites

Evidence of Black Hole at the center of galaxy M87
      Period of Satellites in Circular Orbit
• Period of a satellite = Time required to make
one orbital revolution
                                                  Geo-Synchronous Satellites

     GM E
    GM E 2 r
     r    T
     2 r 2
      GM E

  Kepler ' s Third Law :T  r         2
  Apparent Weightlessness and Artificial Gravity

the apparent weight in the satellite is zero, just as it is in the freely falling
elevator. The only difference between the satellite and the elevator is that the
satellite moves on a circle, so that its “falling” does not bring it closer to the earth. In
contrast to the apparent weight, the true weight is the gravitational force (F =
GmME/r2) that the earth exerts on an object and is not zero in a freely falling
elevator or aboard an orbiting satellite.
                         Artificial Gravity

                            The surface of the rotating space station pushes on an
                            object with which it is in contact and thereby provides
                            the centripetal force that keeps the object moving on a
                            circular path.

The outer ring (radius = r0) of this rotating space laboratory simulates gravity
on earth, while the inner ring (radius = r1) simulates gravity on Mars.
Vertical Circular Motion

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