badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12th pass

                        

What is the moment of intertia of a disc about one of its diameters?

one month ago

Answers : (2)

Rituraj Tiwari
askIITians Faculty
1789 Points
							We assume the moment of inertia of the disc about an axis perpendicular to it and through its centre to be known;it isMR2/2, where M is the mass of the disc and R is its radius.
The disc can be considered to be a planar body. Hence the theorem of perpedicular axes is applicable to it. As shown in Fig., we take three concurrent axes through the centre of the disc, O as thex,y,zaxes;xandy-axes lie in the plane of the disc andzis perpendicular to it. By the theorem of perpendicular axes,
Iz​=Ix​+Iy​
Now,xandyaxes are along two diameters of the disc, and by symmetry the moment of inertia of the disc is the same about any diameter. Hence
Ix​=Iy​
andIz​=2Ix​
ButIz​=MR2/2
So finally,Ix​=Iz​/2=MR2/4
Thus the moment of inertia of a disc about any of its diameter isMR2/4.
one month ago
Vikas Amritiya
askIITians Faculty
158 Points
							

Dear student

We assume the moment of inertia of the disc about an axis perpendicular to it and through its centre to be known; it is MR2/2, where M is the mass of the disc and R is its radius.
The disc can be considered to be a planar body. Hence the theorem of perpedicular axes is applicable to it. As shown in Fig., we take three concurrent axes through the centre of the disc, O as the x,y,z axes ;x and y-axes lie in the plane of the disc and z is perpendicular to it. By the theorem of perpendicular axes,
Iz=Ix+Iy
Now, x and y axes are along two diameters of the disc, and by symmetry the moment of inertia of the disc is the same about any diameter. Hence
Ix=Iy
and Iz=2Ix
But Iz=MR2/2
So finally, Ix=Iz/2=MR2/4
Thus the moment of inertia of a disc about any of its diameter is MR2/4.

Best wishes
one month ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 110 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details