Question

The radius of gyration of a ring about the tangent perpendicular to its plane is ______.

Answer 1

The moment of inertia of a uniform circular disk about the centroidal axis in the plane of the disk is:

IC=14mR2IC=14mR2

Use the parallel axis theorem to determine the moment of inertia about a line tangent to the disk:

IY=IC+md2IY=IC+md2

where d= perpendicular distance from the tangent line to the centroidal axis

therefore, d=R

IY=IC+mR2IY=IC+mR2

or

IY=14mR2+mR2=54mR2IY=14mR2+mR2=54mR2

The radius of gyration k=Im−−√k=Im

or

k=(54)mR2m−−−−−−√k=(54)mR2m=5R24−−−√5R24

or

k=5√2R

finally it may be 1.414*radius of ring

Answer 2

here is your answer dude