Circle moment of inertia Find the principal moments of inertia of a circle of radius $R$ and mass $m$. Use the integration over the circle length. (Hint: first define the infinitesimal moment of inertia). The inertia moment is a measure of how a body that has certain dimensions, opposes to changes in rotation motion, exactly

# Category: Moment of inertia

## Moment of inertia of figure

Determine the moment of inertia of the area about the x axis. Answer $S = \int dS = \int (from 0 to 1) Y*dx = \int(from 0 to 1) \sqrt{x}*dx =(2/3)*x^3/2 =2/3 m^2$Total mass $M = \rho*z*S$ $\rho$ is density, $z$ is the third coordinate infinitesimal mass is $dm = M/S *dS = M*(3/2)

## Moment of Inertia Questions

1. Trucks can be run on energy stored in a rotating flywheel, with an electric motor getting the flywheel up to its top speed of $200\pi$ rad/s. One such flywheel is a solid, uniform cylinder with a mass of 500kg and a radius of 1m. if the truck uses an average power of 8kW, for

## Inertia Moment (Homework 3-103)

1. A hollow sphere (M = 3 kg, R = 60 cm) is rolling down an inclined surface with a height of 2.0 meters and an inclined angle of 25 degrees.a) find the moment of inertia of the sphere.b) find the speed of the center of the mass when it reaches the bottom of the