Question

2. The moment of inertia of a uniform circular disc about a tangent in its own plane is 5/4MR? where M is the mass and R is the radius of the disc. Find its moment of inertia about an axis through its centre and perpendicular to its plane.​

Answer 1

Answer :

The moment of inertia about an axis through its centre and perpendicular to its plane is 1/2 MR²

Step-by-step Explanations :

Given : moment of inertia of a uniform circular disc about a tangent in its

own plane = 5/4MR²

To find : moment of inertia about an axis through its centre and

perpendicular to its plane = ?

Let ID be the M.I. of the disc about its diameter then by theorem of parallel axis,

IT = ID + MR²

Where, IT is moment of Inertia of a uniform circular disc about a tangent

ID = IT - MR²

ID = 5/4 × MR² - MR²

ID = 1/4 × MR²

Using theorem of perpendicular axis,

I = ID + ID

Where,.

I be the moment of Inertia about an axis through its centre and perpendicular to its plane

I = 2 × ID

Substituting the value of ID in above equation we get,

I = 2 × 1/4 × MR²

I = 1/2× MR²

Hence , The moment of inertia about an axis through its centre and perpendicular to its plane is 1/2 MR²