Chapter 8, Problem 73A

To determine

To explain:The reason for more rolling of vehicle with larger diameter wheels in comparison with the vehicle with smaller diameter wheels.

Answer to Problem 73A

The vehicle with larger diameter wheels rolls more in comparison with the vehicle with smaller diameter wheels as the wheels with larger radius is more unstable in comparison to the wheels with smaller radius.

Explanation of Solution

Introduction:

Consider a circular object (say a wheel), the centre of mass of the object is the point in the circular object where the whole mass of the circular object appears to be concentrated.

Consider a vehicle with wheels rolling on the road surface.

The centre of mass of a circular wheel is concentrated at the centre of the wheel. That is the centre of mass is located at a distance equal to radius of the wheel from the road surface.

The rolling of the wheel is because of the instability of the wheel. The instability of the wheel depends on the distance of the centre of mass from the road surface. In other words, the instability of the wheel depends on the radius of the wheel.

Larger the radius of the wheel, greater will be the instability of the wheel which results in more rolling of the wheel over the surface of the road.

Hence, the vehicle with larger diameter wheels rolls more in comparison with the vehicle with smaller diameter wheels as the wheels with larger radius is more unstable and tends to roll more in comparison to the wheels with smaller radius (which is more stable and tends to roll less).

Conclusion:

Thus, the vehicle with larger diameter wheels rolls more in comparison with the vehicle with smaller diameter wheels as the wheels with larger radius is more unstable in comparison to the wheels with smaller radius.