IB Physics Omega in Simple Harmonic Motion

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Many good Physics students are confused when ⍵ is used in simple harmonic motion (SHM) questions. How can something moving in a straight line have an angular velocity ⍵? In SHM it is best to call ⍵ the angular frequency of the motion. SHM is the projection of uniform circular motion (UCM) onto a diameter of the circle.

  1. In Physics what is the name of the quantity that has the symbol ⍵?
  2. What is the SI unit for ⍵?
  3. Imagine that an object is moving in uniform circular motion (UCM) of radius 1.0 m and period 2.0 s. You are watching the object from the side and the object appears to be moving in simple harmonic motion. (a) what is the amplitude of the SHM? (b) what is the period of the SHM? (c) what is the angular velocity of the UCM? (d) what is the angular frequency of the SHM? (1.0 m, 2.0 s, 𝜋 rad s-1, 𝜋 rad s-1).
  4. The radius r of the circular path of a particle moving in UCM is the amplitude x0 of the image of the particle moving in SHM in a straight line along a diameter of the circle.
  5. The angle turned through in a time t by a particle moving in UCM is 𝜽 = ⍵t.
  6. The displacement of a particle from the equilibrium position in SHM is the component of the radius vector in UCM along the direction of the SHM. If at t=0, x=x0 then x = x0 cos(⍵t). If at t=0, x=0 and the particle is moving in the positive direction then x = x0 sin(⍵t). If at t=0, x=0 and the object is going in the negative direction then x = -x0 sin(⍵t).
  7. The speed of a particle moving in UCM is given by v = ⍵r. In SHM the velocity is the component of the UCM velocity vector along the direction of the SHM. If at t=0, x=x0 then v = -⍵x0 sin(⍵t). If at t=0, x=0 and the object is moving in the positive direction then v = ⍵x0 cos(⍵t). If at t=0, x=0 and the object is moving in the negative direction then v = - ⍵x0 cos(⍵t).