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Constraint Equation of a rolling of cylinder

  1. Nov 7, 2015 #1
    I was going through this example from by book, where a cylinder of radius 'r' is rolling inside of another cylinder of radius 'R' without slipping.It says the constraint equation should be
    rθ = (R-r)φ
    where θ = angle of rotation of cylinder of radius 'r'
    φ = angle subtended at the centre of the cylinder of radius 'R'

    I am not getting this. Shouldn't it be rθ = Rφ ....??? To me it looks like if we deduct 'r' from 'R' then
    will be greater than (R-r)φ . Please correct me.
  2. jcsd
  3. Nov 7, 2015 #2


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    Try an example where ##R = 4## and ##r = 1##

    How many times does the smaller cylinder rotate to circumscribe the inside of the larger cylinder once?
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