CHAPTER
8
ROTATIONAL KINEMATICS
ANSWERS TO FOCUS ON CONCEPTS QUESTIONS
1.
(d)
Using Equation 8.1 (
θ
= Arc length / Radius) to calculate the angle (in radians) that each
object subtends at your eye shows that
θ
Moon
= 9.0 × 10
−3
rad,
θ
Pea
= 7.0 × 10
−3
rad, and
θ
Dime
= 25 × 10
−3
rad.
Since
θ
Pea
is less than
θ
Moon
, the pea does not completely cover your
view of the moon.
However, since
θ
Dime
is greater than
θ
Moon
, the dime does completely
cover your view of the moon.
2.
2.20 cm
3.
38.2 s
4.
(a)
An angular acceleration of zero means that the angular velocity has the same value at all
times, as in statements A or B.
However, statement C is also consistent with a zero angular
acceleration, because if the angular displacement does not change as time passes, then the
angular velocity remains constant at a value of 0 rad/s.
5.
(c)
A non-zero angular acceleration means that the angular velocity is either increasing or
decreasing.
The angular velocity is not constant.
6.
(b)
Since values are given for the initial angular velocity
0
, the final angular velocity
, and
the time
t
, Equation 8.6 [
1
0
2
t
] can be used to calculate the angular displacement
θ
.
7.
32 rad/s
8.
88 rad
9.
(c)
According to Equation 8.9 (
v
T
=
r
), the tangential speed is proportional to the radius
r
when the angular speed
is constant, as it is for the earth.
As the elevator rises, the radius,
which is your distance from the center of the earth, increases, and so does your tangential
speed.
10.
(b)
According to Equation 8.9 (
v
T
=
r
), the tangential speed is proportional to the radius
r
when the angular speed
is constant, as it is for the merry-go-round.
Thus, the angular
speed of the second child is
T
2.1 m
2.2 m/s
1.4 m
v
.

Chapter 8
Answers to Focus on Concepts Questions
379
11.
367 rad/s
2
12.
(e)
According to Newton’s second law, the centripetal force is given by
c
c
F
ma
, where
m
is the mass of the ball and
a
c
is the centripetal acceleration.
The centripetal acceleration is
given by Equation 8.11 as
a
c
=
r
2
, where
r
is the radius and
is the angular speed.
Therefore,
2
c
F
mr
, and the centripetal force is proportional to the radius when the mass
and the angular speed are fixed, as they are in this problem.
As a result,
c
33 cm
1.7 N
12 cm
F
.
13.
(d)
Since the angular speed
is constant, the angular acceleration
is zero, according to
Equation 8.4.
Since
= 0 rad/s
2
, the tangential acceleration
a
T
is zero, according to
Equation 8.10.
The centripetal acceleration
a
c
, however, is not zero, since it is proportional
to the square of the angular speed, according to Equation 8.11, and the angular speed is not
zero.

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- Physics, Rotation, Angular velocity, Velocity