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SHM · Lecture 18 of 26

Physical pendulum and torsional pendulum

By Lalit, IIT Madras

Physical and torsional pendulums for JEE SHM: T = 2 π root(I/mgd) for a hinged rod and a semicircular disc, and the least period at d = K.

Watch lecture 18

A rod hangs from a hinge at the top, tilted by an angle θ in a vertical plane, with its weight mg at the middle and a horizontal spring of constant k on each side of its lower end, beside the boxed formula ω² = 6k/m + 3g/(2L).

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What this lecture covers

For a physical pendulum the weight acts at the centre of mass, and its torque about the hinge gives T = 2 π root(I/(m g d)). Plotting a hinged rod's period against the hinge distance finds the least period at d = K, and a semicircular disc follows. Springs on a hinged rod add restoring torque, and in a vertical plane the weight adds its own. Twisting a wire gives the torsional pendulum, T = 2 π root(I/C), with no small-angle step.

In this lecture

  1. Play from The physical pendulum and its torque
  2. Play from Time period T = 2 π √(I/(m g d))
  3. Play from Rod hinged at one end; least period
  4. Play from A semicircular disc as a pendulum
  5. Play from A rod held by two springs
  6. Play from The same arrangement, vertical plane
  7. Play from Springs at two different points
  8. Play from The torsional pendulum, set up
  9. Play from Torsional pendulum: T = 2 π √(I/C)
  10. Play from Recap: two kinds of pendulum