The moment of inertia of a solid sphere about a diameter is 2/5mr2,find the moment of inertia of the sphere about a tangent
Answers
(1) Given,
Moment of inertia of the sphere about its diametre = (2/5)mR²
Use, parallel axis theorem ,
Moment of inertia of the sphere about tangent = I + mR²
= (2/5)mR² + mR²
= (7/5)mR²
(B) given,
Moment of inertia of disc of mass m and radius R about any of its diametre = mR²/4
See the figure ,
Moment of inertia about diametre = Ix = Iy= (1/4)mR²
Use , perpendicular axis theorem ,
We know, Iz = Ix + Iy
Where Iz is moment of inertia about perpendicular axis of plane of disc .
Iz = (1/4)mR² + (1/4)mR²
= (1/2)mR²
Now, moment of inertia of disc about passing through a point of its edge
______________________________
Use , parallel axis theorem ,
I = Iz + mR²
= (1/2) mR² + mR²
= (3/2)mR²
the property of matter by which it retains its state of rest or its velocity along a straight line so long as it is not acted upon by an external force. an analogous property of a force: electric inertia.