# Critical Angular Velocity of Tilted Rotation

**Electricity and Magnetism**Level 5

The top in this case is a hollow octahedron of mass \(m\), charge \(q\) and side \(s\) and the magnetic field has a magnitude \(B\) then the critical angular velocity with which the top has to be spun (about an axis passing through two opposite vertices of the octahedron) can be represented as \[\omega=a\frac{mg}{qsB}\] then find the units digit of [100a]

**Assumptions**

- The point of contact i.e. vertex is stationary mass and charge is uniformly distributed along the faces.
- Refer to gyro -magnetic ratio rather that calculating magnetic moment. For a octahedron ratio of square of radius of gyration to the square is side \(s\) is \( 5/9\).
- \(\left[x\right]\) represents the greatest integer function.
- In both of the cases the tops are rotating in anti clockwise sense, (not as shown in the figure which is clockwise)