Question

A uniform disc of radius a has a hole of radius b at a distance c from the centre as shown. If the disc is free to rotate about a rod passing through the hole b, then find the MOI about the axis of rotation.

• A. $\frac { M } { 2 } \left( a ^ { 2 } + b ^ { 2 } + \frac { 2 c ^ { 2 } a ^ { 2 } } { a ^ { 2 } - b ^ { 2 } } \right)$
• B. M $\left( a ^ { 2 } + b ^ { 2 } + \frac { c ^ { 2 } a ^ { 2 } } { a ^ { 2 } - b ^ { 2 } } \right)$
• C. $\frac { M } { 2 } \left( a ^ { 2 } + b ^ { 2 } + \frac { c ^ { 2 } a ^ { 2 } } { a ^ { 2 } - b ^ { 2 } } \right)$
• D. None

Answer 1

Answer: (A)

$\frac { M } { 2 } \left( a ^ { 2 } + b ^ { 2 } + \frac { 2 c ^ { 2 } a ^ { 2 } } { a ^ { 2 } - b ^ { 2 } } \right)$

Answer 2

Let ρ be the mass per unit area. Then MOI of the disc about O'I = πρa² + π ρa²(c²) - πb²ρ$\left( \frac { b ^ { 2 } } { 2 } \right)$

=

=

and ρ =

= =