Page 184 - Fisika Terapan for Engineers and Scientists

384 CHAPTER 12 Rotation of a Rigid Body

✔ Checkup 12.5
(a) z

QUESTION 1: What is the moment of inertia of a rod of mass M bent into an arc of a
circle of radius R when rotating about an axis through the center and perpendicular to
the circle (see Fig. 12.19a)?
QUESTION 2: Consider a rod rotating about (a) an axis along the rod, (b) an axis per-
(b)
pendicular to the rod through its center, and (c) an axis perpendicular to the rod through
its end. For which axis is the moment of inertia largest? Smallest?
QUESTION 3: What is the moment of inertia of a square plate of mass M and dimen-
sion L L rotating about an axis along one of its edges (see Fig. 12.19b)? What is
the moment of inertia if this square plate rotates about an axis through its center par-
allel to an edge?
QUESTION 4: A dumbbell consists of two particles of mass m each attached to the
ends of a rigid, massless rod of length l (Fig. 12.19c). Assume the particles are point
particles. What is the moment of inertia of this rigid body when rotating about an
axis through the center and perpendicular to the rod? When rotating about a parallel
axis through one end? Are these moments of inertia consistent with the parallel-axis
(c)
theorem?
QUESTION 5: According to Table 12.3, the moment of inertia of a hoop about its sym-
2
metry axis is I CM MR . What is the moment of inertia if you twirl a large hoop
FIGURE 12.19 (a) A rod bent into an around your finger, so that in essence it rotates about a point on the hoop, about an
arc of a circle of radius R, rotating about axis parallel to the symmetry axis?
its center of curvature. (b) A square plate 2 2 3 2
(A) 5MR (B) 2MR (C) MR .
rotating about an axis along one edge. 2
2 1 2
(c) A dumbbell. (D) MR (E) MR .
2

SUMMARY

PROBLEM-SOLVING TECHNIQUES Angular Motion (page 375)

DEFINITION OF ANGLE (in radians) [arc length] s y
f (12.1)
[radius] R

R s

O x

ANGLE CONVERSIONS 1 revolution 2p radians 360

AVERAGE ANGULAR VELOCITY ¢f
(12.2)
¢t

INSTANTANEOUS ANGULAR VELOCITY df
(12.3)
dt