Chapter 8
Part 1 of 1
Example Problems & Solutions
(useful for homework)
3
• 3. A pitcher throws a curveball that
reaches the catcher in 0.6 s. The ball
curves because it is spinning at an
average angular velocity of 330 rev/min
(assumed constant) on its way to the
catcher’s mitt. What is the angular
displacement of the baseball (in radians)
as it travels from the pitcher to the catcher
?
13
• 13. The drawing (page 242, problem 13 of your
textbook) shows a device that can be used to
measure the speed of a bullet. The device
consists of two rotating disks, separated by a
distance of d=0.85 m, and rotating with an
angular speed of 95.0 rad/s. The bullet first
passes through the left disk and then through
the right disk. It is found that the angular
displacement between the two bullet holes is
theta=0.24 rad. From these data, determine the
speed of the bullet.
17
• 17. The drill bit of a variable-speed electric
drill has a constant angular acceleration of
2.5 rad/s2. The initial angular speed of the
bit is 5.00 rad/s. After 4.0 seconds, (a)
what angle has the bit turned through, and
(b) what is the bit’s angular speed ?
25
• 25. A spinning wheel on a fireworks display is
initially rotating in a counterclockwise direction.
The wheel has an angular acceleration of -4.0
rad/s2. Because of this acceleration, the angular
velocity of the wheel changes from its initial
value to a final value of -25.0 rad/s. While this
change occurs, the angular displacement of the
wheel is zero. (Note the similarity to that of a ball
being thrown vertically upward, coming to a
momentary halt, and then falling downward to its
initial position.) Find the time required for the
change in the angular velocity to occur.
29
• 29. A string trimmer is a tool for cutting
grass and weeds; it utilizes a length of
nylon string that rotates about an axis
perpendicular to one end of the string. The
string rotates at an angular speed of 47
rev/s, and its tip has a tangential speed of
54 m/s. What is the length of the rotating
string ?
35
• 35. A person lowers a bucket into a well by
turning the hand crank, as the drawing
(page 244, problem 35 in your textbook)
illustrates. The crank handle moves with a
constant tangential speed of 1.2 m/s on its
circular path. Find the linear speed with
which the bucket moves down the well.
39
• 39. A race car travels with a constant
tangential speed of 75 m.s around a
circular track of radius 625 m. Find (a) the
magnitude of the car’s total acceleration
and (b) the direction of its total
acceleration relative to the radial direction.
45
• 45. An electric drill starts from rest and
rotates with a constant angular
acceleration. After the drill has rotated
through a certain angle, the magnitude of
the centripetal acceleration of a point on
the drill is twice the magnitude of the
tangential acceleration. What is the angle
?
47
• 47. A motorcycle accelerates uniformly
from rest and reaches a linear speed of 22
m/s in a time of 9 seconds. The radius of
each tire is 0.28 m. What is the magnitude
of the angular acceleration of each tires ?
55
• 55. Consult Concept-Simulation 8.1 at
www.wiley.com/college/cutnell for help in understanding
the concepts that are important to this problem. Take two
quarters and lay them on a table. Press down on one
quarter so it cannot move. Then, starting at the 12:00
position, roll the other quarter along the edge of the
stationary quarter, as the drawing (page 245, problem 55
in your textbook) suggests. How many revolutions does
the rolling quarter make when it travels once around the
circumference of the stationary quarter ? Surprisingly the
answer is not one revolution. (Hint: Review the
paragraph just before Equation 8.12 that discusses how
the distance trveled by the axle of a wheel is related to
the circular arc length along the outer edge of the
wheel.)