Biomedical Engineering Reference
In-Depth Information
a
b
c
Fig. 4.1
Three wheels with the same mass, but with different shapes. The different mass
distribution about an axis of rotation determines the specific difficulties to reach a given angular
velocity, as well as to stop, if this is the case
Fig. 4.2
A particle of mass
m
moving in a circular path.
It sweeps out an angle
Δ
θ
in
a time interval
Δ
t
v
S
m
v
R
interval in applying the same torque, wheel (c) will have performed more
revolutions than wheel (b) and the number of revolutions of wheel (a) will be the
smallest, as it has the greatest moment of inertia
I.
Let us see how we can write a mathematical expression that allows us to define
moment of inertia. For this, let us analyze a particle of mass
m
rotating with an
angular velocity
, about an axis of rotation, shown in Fig.
4.2
(larger circumfer-
ence). The angular velocity, described by (
4.3
), is given by the rate at which
ω
θ
changes with time
t
:
ω ¼
Δ
θ
Δ
t
:
(4.3)
The angular velocity
ω
in the SI must be expressed in radians per second (rad/s).
360
. We remember that
Note that 2
f
,with
f
the
rotational frequency, measured in rotations per second (rps), which receives a
special name hertz, shortened Hz, in the SI and hence 1 Hz
π
rad
¼
6.28 rad
¼
ω ¼
2
π
s
1
.
¼
1/s
¼
S
of the particle
along the circular path divided by the radius
R
. Considering that the translational
The angular displacement
Δ
θ
corresponds to the displacement
Δ
