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).

IB SL Physics Poorly Answered Questions 3

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The third sheet of SL Physics questions on areas that are not well answered is given below.

  1. In a longitudinal wave what are the ray directions and direction of the wavefront? What are these directions for a transverse wave?
  2. A string of length 40 cm is fixed at each end and set oscillating in its fundamental mode. What is the phase difference between two points on the string that are 25 cm part?
  3. A particle is moving in simple harmonic motion. Sketch a graph showing the momentum of the particle versus its speed.
  4. When two waves interfere constructively what is the ratio of the intensity produced by the two waves interfering constructively to the intensity due to one of the waves only?
  5. An ammeter and a voltmeter are connected in series with a cell of emf 12 V connected to a 2 Ω resistor. What is the reading on each meter?
  6. An electron is accelerated from rest between two electrodes a distance d apart and the final kinetic energy of the electron is X eV. If the electodes are now placed a distance 2d apart the final kinetic energy of the electron is (a) X/√2, (b) X/2 (c) X (d) 2X
  7. A mass is placed on the end of a light rod of length L and is made to revolve in a vertical plane at a constant speed. At what point in the path is the force exerted by the rod on the mass maximum?
  8. Two resistors P and Q are made of the same material and are at the same temperature. P has twice the length of Q and one half the diameter of Q. If the resistance of Q is 2 Ω, find the resistance of P and Q when they are connected in parallel.