Game Development Reference
In-Depth Information
F
p
= Fcos30
F = 10 N
τ = 1.04 N-m
r = 0.12 m
Figure 4-9.
If force is applied at an angle to the moment arm, torque is reduced.
Torque and Angular Acceleration
Newton's second law relates a net external force to a translational acceleration by the equation
F = ma
. There is a corresponding equation in rotational motion that relates a net torque,
t
, on
an object to a resulting angular acceleration,
a
.
t
=
Ia
(4.32)
The quantity,
I
, in Equation (4.32) is known as the
moment of inertia
. Just as mass is a
physical quantity that resists a change in translational motion, moment of inertia is a physical
quantity that resists a change in rotational motion. Mass is a material property. The mass of an
object depends on what material the object is made of and how much material there is. Moment
of inertia is both a material and a geometrical property. The moment of inertia of an object
depends on the mass of the object and on the shape of the object.
The conclusions that can be taken from Equation (4.32) are similar to those that can be
taken from Newton's second law. If there is no net torque on an object, there is no angular
acceleration, and the angular velocity of the object is either zero or a constant. If they are subjected
to the same torque, an object with a large moment of inertia will have a smaller angular accel-
eration than an object that has a small moment of inertia.
Torque, moment of inertia, and angular acceleration are vector quantities and can be
divided into components acting about the three axes of rotation defined by a particular frame
of reference. The value of the moment of inertia will depend on which axis of rotation is being
considered, the shape of the object, and the distribution of mass within the object. Moments of
inertia for some common objects are shown in Table 4-2. The
m
term in the moment of inertia
expressions is the mass of the object.
