Starting with the formula for the moment of inertia of a rod rotated around an axis through one end perpendicular to its length ( I = Mℓ 2 / 3) , prove that the moment of inertia of a rod rotated about an axis through its center perpendicular to its length is I = Mℓ 2 / 12 . You will find the graphics in Figure shown useful in visualizing these rotations. In statics, the net torque is zero, and there is no angular acceleration. In rotational motion, net torque is the cause of angularacceleration, exactly as in Newton's second law of motion for rotation.AxisHoop aboutcylinder axisAxisAnnular cylinder(or ring) aboutcylinder axisI= MRAxisSolid cylinder(or disk) aboutcylinder axisAxisSolid cylinder(or disk) aboutcentral diameterMR2MR + M12%3DAxisAxisThin rod aboutThin rod aboutaxis throughcenter 1 tolengthaxis through oneend I to length12AxisAxisThinSolid sphere2R about anydiameter2A spherical shellabout anydiameter2MRAxisAxisSlab aboutI axis throughHoop aboutany diametercenterMR2M (a2 + b2)12

Given data: The length of the rod is: L The mass of the rod is: M The elemental mass' distance…

Answered: In statics, the net torque is zero, and…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Starting with the formula for the moment of inertia of a rod rotated around an axis through one end perpendicular to its length ( I = Mℓ 2 / 3) , prove that the moment of inertia of a rod rotated about an axis through its center perpendicular to its length is I = Mℓ 2 / 12 . You will find the graphics in Figure shown useful in visualizing these rotations.

In statics, the net torque is zero, and there is no angular acceleration. In rotational motion, net torque is the cause of angular
acceleration, exactly as in Newton's second law of motion for rotation.
Axis
Hoop about
cylinder axis
Axis
Annular cylinder
(or ring) about
cylinder axis
I= MR
Axis
Solid cylinder
(or disk) about
cylinder axis
Axis
Solid cylinder
(or disk) about
central diameter
MR2
MR + M
12
%3D
Axis
Axis
Thin rod about
Thin rod about
axis through
center 1 to
length
axis through one
end I to length
12
Axis
Axis
Thin
Solid sphere
2R about any
diameter
2A spherical shell
about any
diameter
2MR
Axis
Axis
Slab about
I axis through
Hoop about
any diameter
center
MR2
M (a2 + b2)
12

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