A wheel rolling along a rough horizontal surface with an angular velocity `omega` strikes a rough vertical wall, normally. Find the initial angular velocity, as it tends to roll up the wall (neglect any slippage) due to impulse.

Explanation

Figure shows the two situation of a rolling wheel before and after its striking the wall.
If `C_(2)` is the point on the wall where the wheel strikes, then the impulseive force `F` passes through it. Moreover, the weight of the wheel `mg` and the normal reaction offered by the horizontal surface on the wheel to balance each other. So, the angular momentum of the wheel remains conserved about point `C_(2)`.

`:.` Initial agular mometum `=` final agular momentum
`:. Iomega_(0)=Iomega+mvr`
[where `omega` and `v` are the angular and linear speeds of the wheel, just after its striking]
Since slipage is prevented so `v=omegar`
`:. Iomega_(0)=Iomega=momegar^(2)`
`implies(mr^(2)omega_(0))/2=(mr^(2)omega)/r=momegar^(2)`
`implies omega=(omega_(0))/3`