PHY009 · Mechanics · Classes 11–12 + College
Moment of inertia
Objective: To compare the moments of inertia of different shapes and see how they resist angular acceleration.
🧰 Apparatus
- Disc, ring and sphere of equal mass and radius
- Axle with a string and falling mass
- Stopwatch
- Metre scale
📐 Formulas and SI units
τ = Iα
I: disc ½MR², ring MR², solid sphere ⅖MR², rod (centre) ML²/12
💡 Theory
Moment of inertia I measures how hard it is to change rotation. It depends on how far the mass is from the axis: a ring (I = MR²) is harder to spin than a disc (½MR²). Newton's second law for rotation is τ = Iα.
🪜 Procedure
- Mount the disc on the axle and wind the string.
- Let the falling mass apply a steady torque.
- Time how long the disc takes to reach a set speed, or measure α.
- Repeat with the ring and the sphere.
- Calculate I = τ/α and compare with the formulas.
📋 Observations Simulated values
✅ Result and conclusion
A 2 kg disc of radius 0.5 m has I = 0.25 kg m², so a 2 N m torque gives α = 8 rad/s²; the ring accelerates half as fast.
🔬 In a real lab
Axle friction and the string's inertia add errors; real discs have a hub and holes that change I.
⚠️ Safety
Keep fingers, hair and loose clothes away from spinning objects.
❓ Quick check
1. Which spins up fastest with the same torque (same M and R)?
2. Unit of moment of inertia?
3. Moving mass away from the axis makes I…
🏋️ Practice
EasyRing, 1 kg, 0.2 m. I?
Answer: 0.04 kg m²
MediumI = 0.5 kg m², τ = 2 N m. α?
Answer: 4 rad/s²
ChallengeWhy do skaters pull their arms in to spin faster?
Answer: I decreases, so ω increases (angular momentum conserved)