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SHM · Lecture 17 of 26

Angular SHM: torque instead of force

By Lalit, IIT Madras

Angular SHM swaps force for torque: tau = −C θ, then where the angular velocity and angular acceleration peak, for JEE Main and Advanced.

Watch lecture 17

A pendulum swings between −θ0 and θ0 on either side of a dashed vertical equilibrium line, with an arrow Ω at the bob, beside the boxed formulas θ = θ0 sin(ωt + φ) and Ω = θ0 ω cos(ωt + φ) and the note ω ≠ Ω.

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What this lecture covers

Net torque and angular acceleration replace force and acceleration, with θ measured from equilibrium. A restoring torque tau = −C θ defines angular SHM and fixes ω, and the solution θ = θ₀ sin(ω t + φ) carries an amplitude and a phase. Differentiating gives the angular velocity Omega, which differs from ω and peaks at equilibrium as ω θ0. Angular acceleration α = −ω² θ is largest at the extremes, ω² θ0. The pendulum is then redone by torque.

In this lecture

  1. Play from Angular oscillation and net torque
  2. Play from Angular displacement, restoring torque
  3. Play from Restoring torque: tau = −C θ
  4. Play from Angular frequency ω = √(C/I)
  5. Play from The solution: θ against time
  6. Play from Angular velocity, capital Omega
  7. Play from Omega = ω √(θ₀² − θ²)
  8. Play from Angular acceleration and its maximum
  9. Play from Linear to angular: I replaces mass
  10. Play from The pendulum through the torque method