
Find the moment of inertia of a ring of mass and radius about an axis passing through its centre and making an angle of with its plane.

Answer
458.7k+ views
1 likes
Hint: To solve this question, we need to have a knowledge about the parallel axis theorem. We will also have to use some other property because this will not be enough to solve this question. Using these two theorems we can find out the moment of inertia of the ring about an axis passing through its centre and making an angle of with its plane.
Complete answer:
By using parallel axis theorem, we can say that moment of inertia along the axis will be equal to the moment of inertia along the axis due to symmetry. Now, let us see the following diagram which makes this statement clearer. And let us assume that an axis passes perpendicularly to the plane formed by the axis and axis. This plane would pass along the diameter of the ring as such:
Now, we know that the moment of inertia of a ring about an axis passing through its diameter is:
We also know that:
Here are the moment of inertia about the three mutually perpendicular and intersecting axes,
is the mass of the particle,
And is the distance from intersection
As we earlier said that , hence:
Thus, the moment of inertia of ring of mass and radius about an axis passing through its centre and making an angle of with its plane is .
Note:
According to the parallel axis theorem, the moment of inertia of a body about an axis is the sum of moment of inertia of the body about a parallel axis that passes through the center of mass of the body and the product of the mass of the body with the square of distance of the body from the parallel axis that passes through the center.
Complete answer:
By using parallel axis theorem, we can say that moment of inertia along the

Now, we know that the moment of inertia of a ring about an axis passing through its diameter is:
We also know that:
Here
And
As we earlier said that
Thus, the moment of inertia of ring of mass
Note:
According to the parallel axis theorem, the moment of inertia of a body about an axis is the sum of moment of inertia of the body about a parallel axis that passes through the center of mass of the body and the product of the mass of the body with the square of distance of the body from the parallel axis that passes through the center.
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Trending doubts
The flightless birds Rhea Kiwi and Emu respectively class 11 biology CBSE

1 litre is equivalent to A 1000mL B 100cm3 C 10mL D class 11 physics CBSE

A car travels 100 km at a speed of 60 kmh and returns class 11 physics CBSE

Name the Largest and the Smallest Cell in the Human Body ?

Explain zero factorial class 11 maths CBSE

In tea plantations and hedge making gardeners trim class 11 biology CBSE
