A cylinder rolls on the planks `A` and `B` without relative sliding. If the planks move with velocities `-2vhati, vhati` respectively and the plank `A` has acceleration `veca(=ahati)`, find the: (a) `v_(C)` and `v_(Q)` and (b) `a_(C)` and `a_(Q)`.

Answer

`a/2hatj`

Explanation

`vecv_(C)=vecv_(CB) +vecv_(B)=Romegahat+vhati`
`=[-R((3v)/(2R))+v]hati=-v/2hati`
`vecv_(Q)=vecv_(QC)=vecv_(C)=Romegaj-v/2hati=-R((3v)/(2R))hatj-v/2hati`
`=-3/2vhatj-v/2hati`

b. `a_(C)=a/2hati`
`veca_(Q)=veca_(QC)+veca_(CB)+veca_(B)=Romega^(2)hati+Ralpha hatj +a/2 hati`
where `alpha=a/(2R)` and `omega=(3v)/(2R)`
`veca_(Q)=(a/2-(9v^(2))/(4R))hati+a/2hatj`