Page 143 - 4624

magnitude of v is simply v = ω r / B IC , where ω is the angular velocity
B
B
of the body. Due to the circular motion, the direction of v must
B
always be perpendicular to r / B IC .
For example, the IC for the bicycle wheel in Fig. 2-26 is at the
contact point with the ground. There the spokes are somewhat visible,
whereas at the top of the wheel they become blurred. If one imagines
that the wheel is momentarily pinned at this point, the velocities of
various points can be found using v ω= r . Here the radial distances
shown in the photo, Fig. 2-26, must be determined from the geometry
of the wheel.
Determine Location of the IC. To locate the IC we can use the
fact that the velocity of a point on the body is always perpendicular to
the relative position vector directed from the IC to the point. Several
possibilities exist:
1. The velocity v of a point A on the body and the angular
A
velocity ω of the body are known, Fig. 2-27,a. In this case, the IC is
located along the line drawn perpendicular to v at A, such that the
A
distance from A to the IC is r / A IC = v A / ω. Note that the IC lies up and
to the right of A since v must cause a clockwise angular velocity ω
A
about the IC.
2. The lines of action of two nonparallel velocities v and v B
A
are known, Fig. 2-27,b. Construct at points A and B line segments that
are perpendicular to v and v . Extending these perpendiculars to
A
B
their point of intersection as shown locates the IC at the instant
considered.
3. The magnitude and direction of two parallel velocities v and
A
v B are known. Here the location of the IC is determined by
proportional triangles. Examples are shown in Fig. 2-27,c and d. In
both cases r / A IC = v A / ω and r / B IC = v B / ω. If d is a known distance
between points A and B, then in Fig. 2-27,c, r / A IC + r / B IC = d and in
Fig. 2-27,d, r / A IC − r / B IC = d .
4. The magnitude of two parallel velocities v and v are equal.
B
A
It means that the magnitude and direction velocity all points are equal.
Here the IC is located on infinity. The rigid body realizes
instantaneous-translation motion.

143