A wheel of radius r , mass m , and moment of inertial I = mR 2 is pulled along a horizontal surface application of a horizontal force F to a rope unwinding from an axle of radius b as shown in fig. You may assume there is a frictional force between the wheel and the surface such that the wheel rolls without slipping. In the expression I = mR 2 the quantity R is a contact with dimensions of length.
Text Solution
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Sol. Let x be the displacement of the center of mass of the wheel along the horizontal direction and θ the angular displacement of the wheel from an initial direction through its center of mass.
The equations of motion of the wheel are (fig.)
m 
= F – f
I 
= Fb + fr
The constraint for on sliding is 
= r 
or 
= r 
. Hence
= Fb + (F – m 
) r,
or 
= 
, Ans.
which is the linear acceleration of the wheel.
The frictional force is
f = F – m 
= F 
= 
. Ans.
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