Problem

In Prob. 7.1 you were told to neglect the rotational inertia of the front wheels—would inc...

In Prob. 7.1 you were told to neglect the rotational inertia of the front wheels—would including it really make a difference? Let’s see.

A certain roadster can go from 0 to 60 mph in 7.0 s, the weight of the car (including the two front wheels) is 2750 lb, the weight of each of its front wheels is 47 lb, and they each have a mass moment of inertia IG of 0.989 slug · ft2. To determine the effect of the rotational inertia of the front wheels, perform the following analysis:

(a) Isolate one of the front wheels and determine the friction force that must be acting on the wheel for it to accelerate as given. Hint: The weight of the car on the front wheel is not known, but it is not needed to find the friction force since we are assuming that friction is sufficient to prevent slipping of the front wheels.

(b) Next, note that it is the friction force that makes the rotational motion of each front wheel possible. In addition, note that if the mass moment of inertia IG of the front wheels were zero, then the friction force would be zero. Therefore, by neglecting the rotational inertia of the front wheels, the car would not be slowed by the friction forces found in (a). In other words, when we do account for the rotational inertia of the front wheels, we can then conclude that there is a force equal to twice the friction force that is “retarding” the motion of the car. Use this fact, and your result from (a), to determine the 0 to 60 mph time of this same roadster with front wheels that have no rotational inertia.