A cart with mass M has four wheels (idealized as uniform discs), each of radius r and mass m, arranged symmetrically with respect to the cart. Find the acceleration of the cart when a horizontal force F is applied on it. There is no slipping between the wheels and the horizontal road.
2. Homework Equations
a = rα
Γ = Iα
(M+4m)a = F-4f.
The Attempt at a Solution
I first calculated the linear acceleration w.r.t. ICM using a = rα. The net torque on any disc will be due to frictional force and will be equal to f*r (f=frictional force). I equated this to Iα and then finally used (M+4m)a = F-4f to calculate the value of a.
In this problem, the wheels are rolling on the ground without slipping. In that case, shouldn't the friction on the lower most part be equal to zero. Why are we taking friction into account? Also, assuming we take friction into account, was what I did above correct?
Edit: Is there friction there in order to prevent slipping?