New Zealand Scholarship · Physics and Chemistry

Rotational Dynamics, Simple Harmonic Motion, Gravity and Wave Interference

35 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 35 questions

  1. A figure skater spins with angular velocity omega_1 with arms outstretched. When she draws her arms inwards, her moment of inertia decreases by 40%. What happens to her rotational kinetic energy?
  2. A mass-spring system executes simple harmonic motion with amplitude A. At what displacement x from equilibrium is the kinetic energy equal to the potential energy?
  3. What is the orbital speed of a satellite in circular orbit around Earth at radius r, where M is Earth's mass?
  4. In a double-slit interference experiment with slit separation d and light wavelength lambda, what is the path difference for the third dark fringe?
  5. A uniform rod of length L and mass M is hinged at one end and released from horizontal rest. What is its initial angular acceleration (I = (1/3)ML^2)?
  6. What is the period of a simple pendulum of length l in a region of gravitational acceleration g?
  7. A solid cylinder (I = 0.5MR^2) rolls down an incline of height h without slipping. What is its linear speed at the bottom?
  8. Two sound waves with frequencies 440 Hz and 444 Hz interfere. What beat frequency is heard by an observer?
  9. A car sounds its horn at 500 Hz while approaching a stationary observer at 20 m/s. If the speed of sound is 340 m/s, what frequency is observed?
  10. What is the escape velocity from the surface of a spherical planet of mass M and radius R?
  11. In simple harmonic motion, what is the phase difference between displacement and acceleration?
  12. A diffraction grating has 500 lines per mm. What is the highest order diffraction maximum for light of wavelength 600 nm?
  13. How does the gravitational field strength g vary inside a uniform solid sphere of radius R at distance r from the centre (r < R)?
  14. A pipe of length L is open at one end and closed at the other. What is the fundamental wavelength of standing sound waves inside it?
  15. What happens to the period of a mass on a vertical spring if the entire apparatus is transported to the Moon, where gravity is one-sixth of Earth's?
  16. A flywheel with moment of inertia 20 kg m^2 accelerates from rest under a constant torque of 100 N m. What is its angular kinetic energy after 4 seconds?
  17. Why do soap bubbles display vibrant coloured bands when illuminated by white sunlight?
  18. A pendulum clock calibrated at sea level is taken to the summit of Mount Cook. How does the clock run relative to sea level?
  19. What is the condition for resonance to occur in a driven mechanical oscillator with damping?
  20. A 2.0 kg block oscillates on a spring with k = 200 N/m. What is the maximum acceleration of the block if the amplitude is 0.10 m?
  21. A thin spherical shell has mass M and radius R. What is the gravitational potential inside the shell at distance r from the centre (r < R)?
  22. When two coherent light waves of identical amplitude A and phase difference delta interfere, what is the resultant intensity proportional to?
  23. A solid sphere and a hollow sphere of identical mass and radius roll down the same incline from rest. Which reaches the bottom first?
  24. What happens to the fringe width in Young's double-slit experiment when the entire apparatus is immersed in water (refractive index n = 1.33)?
  25. In simple harmonic motion, at what point in the oscillation cycle is the velocity at its maximum magnitude?
  26. A planet orbits the Sun in an elliptical path. According to Kepler's second law, what quantity is strictly conserved for the planet?
  27. What is the tension in a pendulum string of bob mass m and length L as it passes through the lowest point with speed v?
  28. Why does a rotating gyroscope resist changes to the orientation of its rotational spin axis?
  29. What is the total mechanical energy of an undamped simple harmonic oscillator of mass m, spring constant k, and amplitude A?
  30. In an acoustic standing wave formed inside a closed-open tube, what is present at the closed end boundary?
  31. Two simple harmonic motions along the same axis are given by x_1 = 3sin(omegat) and x_2 = 4cos(omegat). What is the amplitude of the resultant motion?
  32. A satellite moves from a low circular orbit to a higher circular orbit around Earth. How do its orbital speed and total mechanical energy change?
  33. What causes the distinctive sound quality or timbre of a musical instrument playing a fundamental pitch of 440 Hz?
  34. What happens to the angular momentum of an isolated rotating planet when tidal forces cause it to deform into an oblate spheroid?
  35. If the distance between two gravitational point masses is doubled, by what factor does the gravitational attraction between them change?

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