Physics · Class 11

Twist a torsional pendulum

Angular SHM occurs when torque is proportional and opposite to angular displacement. A larger rotational inertia gives a longer period; a stronger torsion constant gives a shorter period.

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Twist a torsional pendulum

கோண இடப்பெயர்ச்சிக்கு எதிராக நேர்விகித திருப்புவிசை இருந்தால் கோண எளிய இசை இயக்கம் கிடைக்கும்.

Key notes, relationships and model limits

Key relationship

τ=−κθ; ω=√(κ/I); T=2π√(I/κ).

Remember

Angular SHM occurs when torque is proportional and opposite to angular displacement. A larger rotational inertia gives a longer period; a stronger torsion constant gives a shorter period.

Common trap

Torsion constant has units of torque per radian, not linear spring stiffness.

Model limits

Small angular displacement with a linear torsional restoring torque; no damping. Inertia is about the torsion axis.

What you will learn

Apply the rotational form of a harmonic restoring law.

Try the experiment

Try both scenarios, change one control, and predict the result before checking the graph and readouts.

Think of it this way

Change one input while keeping the others fixed, as you would in a controlled experiment.

Worked example

For I=0.05 kg·m² and κ=0.1 N·m/rad, T=2π√0.5=4.443 s. A 15° initial twist stores 0.003427 J.

Why this matters

The model connects twist a torsional pendulum with an observable reading. Check the equation and assumptions before applying it.

Before you start

SI units · algebra · graph reading

Check your understanding

If moment of inertia quadruples with unchanged torsion constant, what happens to period?

It quadruples
It doubles
It halves

Read the explanation

T is proportional to √I.

Course connection: Class XI Chapter 13. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.