SUMMARY
The moment of inertia of a ceiling fan can be calculated using Newton's second law for rotation. Given an angular speed of 2.40 rad/s and a frictional torque of 0.227 Nm that brings the fan to a stop in 6.65 seconds, the angular acceleration can be determined first. By applying the relationship between torque, moment of inertia, and angular acceleration, the moment of inertia can be deduced without needing the radius of the fan.
PREREQUISITES
- Understanding of angular kinematics
- Familiarity with Newton's second law for rotation
- Knowledge of torque and its relationship to angular acceleration
- Basic principles of rotational motion
NEXT STEPS
- Calculate angular acceleration using the formula α = (ω_final - ω_initial) / time
- Apply the formula τ = I * α to find the moment of inertia
- Explore the concept of rotational kinetic energy using K = 1/2 I ω^2
- Study examples of calculating moment of inertia for various shapes and objects
USEFUL FOR
Physics students, mechanical engineers, and anyone interested in understanding rotational dynamics and calculating moment of inertia in practical applications.