Chapter 8
Problems
23
or
The quadratic formula yields
t
= 7.37 s and 42.6 s; therefore, the shortest time needed to
catch the horse is .
34.
REASONING
The angular acceleration
α
gives rise to a tangential acceleration
a
T
according to
(
Equation
8.10).
Moreover, it is given that
a
T
=
g
, where
g
is the magnitude of
the acceleration due to gravity.
SOLUTION
Let
r
be the radial distance of the point from the axis of rotation.
Then,
according to
Equation
8.10, we have
Thus,
35.
REASONING AND SOLUTION

36.REASONINGThe tangential speed vTof a point on a rigid body rotating at an angular speed ϖis given by (Equation 8.9), where ris the radius of the circle described by the moving point. (In this equation ϖmust be expressed in rad/s.) Therefore, the angular speed of the bacterial motor sought in part ais . Since we are considering a point on the rim, rthe radius of the motor itself. In part b,we seek the elapsed timetfor an angular displacement of one revolution at the constant angular velocity ϖfound in part a. We will use (Equation 8.7) to calculate the elapsed time.
is
SOLUTION

Chapter 8
Problems
25
ϖ
t
.

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- Spring '10
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- Angular velocity, Velocity, rad/s, angular displacement, θ moon