Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 643

Description Mass (kg) Center of mass (cm) Dimensions (cm, x × y × z )

Body front 1000 (0, 100, 225) 200 × 80 × 150

Body middle 600 (0, 125, 75) 200 × 130 × 150

Body rear 400 (0, 100, −120) 200 × 80 × 240

Front left wheel 50 (−100, 35, 230) 20 × 70 × 70

Front right wheel 50 (100, 35, 230) 20 × 70 × 70

Rear left wheel 50 (−100, 35, −150) 20 × 70 × 70

Rear right wheel 50 (100, 35, −150) 20 × 70 × 70

Table 12.2. Primitives used to approximate the mass of a truck

The position, mass, and dimensions of these primitives are given by Ta-
ble 12.2.

(a) What are the coordinates of the center of mass of the truck?
(b) Calculate the inertia tensor for each primitive, relative to its cen-
ter of mass. Assume all the primitives have uniform density. (You
will need to find the appropriate formulas online.) Hint: convert the
measurements to meters first.
(c) Use the parallel axis theorem to compute the inertia tensor of the
truck relative to its center of mass.

We love force and we care very little how it is exhibited.
— Ralph Waldo Emerson (1808-1882)