To the plane, let us take an infinitesimally small mass (dm) of length (dx) of Inertia of the ring about an axis passing through its center and perpendicular Us consider a uniform ring of mass M and radius R. The mass is distributed on either side of the origin, the limits for Moment of inertia (I) of the entire rod can be found by integrating dI, (dm) mass of the infinitesimally small length as, dm = λdx = M/ l dx The mass is uniformly distributed, the mass per unit length ( λ ) of the rod is, λ = M/ l Moment of inertia of this rod about an axis that passes through the center ofįirst an origin is to be fixed for the coordinate system so that itĬoincides with the center of mass, which is also the geometric center of the Us consider a uniform rod of mass (M) and length ( l ) as shown in Figure 5.21. The common bulk objects of interest like rod, ring, disc, sphere etc. Get the moment of inertia of the entire bulk object by integrating the aboveĬan use the above expression for determining the moment of inertia of some of The moment of inertia of this point mass can now be The way the mass is distributed around the axis of rotation.įind the moment of inertia of a uniformly distributed mass we have to considerĪn infinitesimally small mass (dm) as a point mass and take its position (r) It depends not only on the mass of the body, but also on But, the moment of inertia of a body is not an In general, mass is an invariable quantity of matter (except for motionĬomparable to that of light). Rotational motion, moment of inertia is a measure of rotational inertia. Translational motion, mass is a measure of inertia in the same way, for For point mass m iĪt a distance r i from the fixed axis, the moment of inertia is given This quantity isĬalled moment of inertia (I) of the bulk object. The expressions for torque and angular momentum for rigid bodies (which areĬonsidered as bulk objects), we have come across a term Σ m i r i 2.
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