A solid cylinder has a mass of M and radius R. If it rolls without slipping on a horizontal surface with a linear speed of v, how high will it roll up an incline of angle θ? Don’t worry about friction. The moment of inertia for a cylinder is (1/2)MR2. Express the vertical height in terms of the given variables M, R, v, θ and g (some might not be used).

Question

A solid cylinder has a mass of M and radius R.  If it rolls without slipping on a horizontal surface with a linear speed of v, how high will it roll up an incline of angle θ?  Don’t worry about friction.  The moment of inertia for a cylinder is (1/2)MR2.  Express the vertical height in terms of the given variables M, R, v, θ and g (some might not be used).

Steve · Answer

its initial KE = 1/2 Mv^2 all that has to go into PE, Mgh so, gh = 1/2 v^2 and the distance rolled is h/sinθ, right? See where that takes you.