Background Information and Techniques - Computer Animation: Algorithms and Techniques - page 472

Instantaneous linear
velocity of particle induced
by angular velocity

Angular velocity of particle
displaced from center of
rotation

Angular velocity vector at
center of rotation

Center of rotation

Position vector of particle
relative to center of rotation

Rotating rigid mass

FIGURE B.52
Motion of particle in a rotating rigid mass.

Second Law: The change of motion of an object is proportional to the forces applied to it.
Third Law: To every action there is always opposed an equal and opposite reaction.

F ¼ ma

(B.102)

d
dt ðmvÞ
F x ¼ ma x
F x ¼ ma y

F ¼

(B.103)

F x ¼ ma z (B.104)

B.7.4 Inertia and inertial reference frames
An inertial frame is a frame of reference (e.g., a local coordinate system of an object) in which the
principle of inertia holds. Any frame that is not accelerating is an inertial frame. In an inertial frame
one observes the laws of motion and has no way of determining whether one is at rest or moving in an
“absolute” sense. (But then, what is “absolute”?)

B.7.5 Center of mass
The center of mass of an object is that point at which the object is balanced in all directions. If an exter-
nal force is applied in line with the center of mass of an object, then the object moves as if all the mass
were concentrated at the center (“ c ”in Figure B.53 ).

B.7.6 Torque
The tendency of a force to produce circular motion is called torque . Torque is produced by a force
applied off-center from the center of mass of an object ( Figure B.54 ) and is computed by
Equation B.105 .

t ¼ r F (B.105)