Why do spheres roll so far? Say you have a sphere and a cuboid, both of equal mass and material. You push both on a ground of the same material over the same period of time with an equal force. Intuition tells you that the sphere would roll much further than the cuboid. Why is this?
The most common model of friction, $F_{\mathrm{fr}}=\mu_k N$, suggests that friction does not depend on surface area, which I understand. Then, if we fit into the equation the coefficient of friction and normal force for each case (the sphere and the cuboid), we would get that the frictional force is equal! So why does it seem like the frictional force on the sphere is so much less than that of the cuboid that it can travel so much further?
 A: The block moves by sliding.  When an object slides, the two surfaces are moving relative to each other and friction acts opposite to the motion.  This opposite force does negative work on the block and slows it down.
While the sphere might slide at first, it will normally be rolling.  When an object is rolling, the two surfaces are not moving relative to each other.  Without relative motion, there is no (kinetic) friction.
In the ideal case (flat surfaces, no deformation, no air resistance), then friction does not act and there is nothing to dissipate the energy.  The object can roll arbitrarily far.  See also: Does friction act on a wheel rolling at a constant speed
A: For any wheel, it undergoes sliding and rolling friction as it moves. Do note that sliding and rolling friction act in opposite directions, so they cancel out. In a circular wheel both of the frictions are roughly equal due to contact at a point, so the wheel experiences little or no friction. However, a square wheel has a relatively large sliding friction due to its large faces, making the friction greater than a circular wheel.
Hence, since circular wheels would experience less friction, there is less work done due to friction, and would possess more kinetic energy for it to move further than say a square-shaped wheel.
