Lab 08: Moment of Inertia and Torque

Learning Objectives

  • Relate torque to angular acceleration in a rotating system.
  • Determine the moment of inertia of a disk, pulley, or rotating platform experimentally.
  • Compare experimental moment of inertia with theoretical values.
  • Identify energy losses due to bearing friction and string slip.

This placeholder is prepared for a complete laboratory experiment on rotational dynamics. It can be adapted for a rotary motion sensor, pulley-and-hanging-mass system, disk-and-axle setup, or torsional apparatus.

Torque

Torque is the rotational effect of a force applied at a perpendicular distance from an axis.

τ=rF\tau = rF

Variables

SymbolDescriptionUnit
τ\tautorqueN·m
rrmoment arm or radiusm
FFapplied forceN

Rotational form of Newton's Second Law

Net torque equals moment of inertia times angular acceleration.

∑τ=Iα\sum \tau = I\alpha

Variables

SymbolDescriptionUnit
IImoment of inertiakg⋅m2kg·m^2
α\alphaangular accelerationrad/s2rad/s^2

Suggested Apparatus

ApparatusPurpose
Rotational platform, disk, or pulleyRotating body under study.
String and hanging massesApplies torque to the system.
Motion sensor or stopwatchMeasures angular acceleration or motion time.
Meterstick or caliperMeasures radius.
BalanceMeasures mass.

Placeholder procedure outline

  1. Measure the mass and radius of the rotating object.
  2. Attach a string to the axle or pulley and connect it to a hanging mass.
  3. Release the mass and record angular acceleration or time of descent.
  4. Compute the applied torque.
  5. Determine experimental moment of inertia using I=τ/αI = \tau/\alpha.
  6. Compare the result with the theoretical moment of inertia for the chosen geometry.
  7. Discuss friction and rotational energy loss.

Data Table Placeholder

TrialRadius, mHanging mass, kgApplied torque, N·mAngular acceleration, rad/s²Experimental II, kg·m²
1
2
3

To complete this lab

Add the selected rotating body formula, sample computation, free-body diagram, and discussion questions about why mass distribution affects moment of inertia.

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