Torsional Oscillations
For angular displacement theta and torsion constant kappa, the restoring torque is -kappa theta and a body of moment of inertia I has omega = sqrt(kappa/I).
Why this shows up in the exam
Torsion pendulums · Frequency change after adding masses · Finding torsion constants or moments of inertia
Learn the idea
A torsion wire supplies restoring torque, making angular frequency depend on torsion constant and rotational inertia. Twisting the suspension stores elastic energy; a body with larger moment of inertia responds more slowly to the same restoring torque.
🧠 Memory hook: Torsion mirrors a spring: torque over angle replaces force over distance.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- tau = -kappa theta — linear torsional restoring torque
- omega = sqrt(kappa/I) — torsional angular frequency
- T = 2 pi sqrt(I/kappa) — torsional oscillation period
How to approach it
- 1Calculate total inertia about the wire
- 2Keep the torsion constant unchanged unless stated
- 3Use a frequency or period ratio to eliminate constants
Common slip-ups that cost marks
- •Using total mass instead of moment of inertia
- •Omitting the added masses' distance squared
- •Confusing angular oscillation frequency with angular displacement
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A mass of 1 kg is attached to a spring of force constant 100 N/m. Find the angular frequency of small oscillations.
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