Chapter 8, Problem 8Q

Mammals that depend on being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8-33). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Figure 8-33

To determine

The reason for the distribution of body mass that helps mammals run faster based on rotational dynamics

Answer to Problem 8Q

Solution:

As the fast moving limb strikes on the ground, the greater angular acceleration provided by the lower moment of inertia will be converted into linear acceleration. It is very advantageous and the mammal does not skid due to this.

Explanation of Solution

The more the body mass is concentrated towards the center of mass of the mammal, the lower is the moment of inertia that needs to be overcome while running.

From the relation, $\text{τ = I}\times \text{α}$

, we see that for the same angular acceleration (α), lower the moment of inertia (I), lower is the torque needed to be provided by the body.