Angular Acceleration

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The angular acceleration a is defined as the rate of change of the angular velocity.  The average angular acceleration is given by

,

The angular velocity changes when the rotation rate is increasing or decreasing and when the axis of rotation changes direction.  The angular acceleration is a vector.
The angular acceleration is defined as the rate of change of the angular velocity.
The angular velocity changes when the rotation rate is increasing or decreasing and when the axis of rotation changes direction.
 

Problem:

  • What is the magnitude of the angular velocity, w, of the second hand of a clock?  What is the direction of w as you view a clock hanging vertically?  What is the magnitude of the angular acceleration of the second hand?
    • Solution:
      The second hand of a clock goes through an angular displacement of 2p in one minute.  Its angular speed is w = 2p/60s = 0.105/s.  The direction of w is perpendicular to the face of the clock, pointing into the face of the clock.  The average angular acceleration of the second hand is zero.

Problem:

  • What is the angular speed, in radians per second, of
    (a) the Earth in its orbit about the Sun, and
    (b) the Moon in its orbit about the Earth?
    • Solution:
      • (a) The earth orbits the sun once every year.  The angular speed of the earth in its orbit about the sun is w = 2p/year = 2p/(365246060s) = 210-7/s.
      • (b) The moon orbits the earth once 27.3 days.  The angular speed of the moon in its orbit about the earth is w=2p/(27.3 days)=2p/(27.3246060s) = 2.710-6/s.