Rotational Kinematics Guided Reading
Chapter 8, pages 206 to 214, Sections 8.1 through 8.3
1. What is the axis of rotation? The center of all circular paths defined by a single, straight line.
2. Define angular displacement (use the simpler definition, not the one in the box). The angle through
which a rigid body rotates about a fixed axis.
3. What is the SI unit for angular displacement? radian (rad)
4. What are the three ways that express angular displacement? Angular displacement is expressed in
degrees, revolutions and radians.
5. What are the conversion factors among the three measurements? In other words, how do you convert
from degrees to radians, radians to revolutions, etc.? Because there are 360º in one full revolution, and
there are 2𝜋 radians in each revolution, we can set up our conversion factors dependent upon what we
want to convert, so we have:
From radians to degrees we use
we use
2𝜋
1 𝑟𝑒𝑣
360º
2𝜋
2𝜋
. From degrees to radians we use 360º. From revolutions to radians
. From radians to revolutions we use
degrees to revolutions, we use
1 𝑟𝑒𝑣
2𝜋
360º
. From revolutions to degrees we use 1 𝑟𝑒𝑣. From
1 𝑟𝑒𝑣
360º
.
6. What are the positive and negative conventions for rotational motion? positive is counter-clockwise
motion while negative is clockwise motion.
7. Copy figure 8.3 with the explanation of the radian measurement.
In radian measure, the angle θ is defined to be the arc
length of s divided by the radius r
8. What is the angular displacement in radians of a disc that has rotated 255º on its axis relative to its
starting point? 4.45 rad
9. If an object spins to a halt, resulting in an angular displacement of 2,513 rads, how many revolutions did
the object turn? 400 rev
10. What is the symbol for angular velocity? ω omega, the Greek symbol
11. What is the equation for angular velocity?
average angular velocity =
𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑒𝑙𝑎𝑝𝑠𝑒𝑑 𝑡𝑖𝑚𝑒
=
𝜃−𝜃𝑜
𝑡−𝑡𝑜
=
𝛥𝜃
𝛥𝑡
12. What are the units for angular velocity? rad/s
13. Copy example 3 “Gymnast on a High Bar” example into your notebooks.
14. What is instantaneous angular velocity? Instantaneous angular velocity is the angular velocity that
exists at any given instant.
15. What is the symbol for angular acceleration? α omega, the Greek symbol
16. What is the equation for angular velocity?
average angular acceleration =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑒𝑙𝑎𝑝𝑠𝑒𝑑 𝑡𝑖𝑚𝑒
=
𝜔− 𝜔𝑜
𝑡−𝑡𝑜
=
𝛥𝜔
𝛥𝑡
17. What are the units for angular acceleration? rad/s2
18. Copy example 4 “A jet Revving Its Engines” into your notebooks.
19. Copy table 8.1 “The Equations of Kinematics for Rotational and Linear Motion” into your notebook.
Compare and contrast the equations.
Both sets of equations can be used to
determine displacement, time, velocities
and accelerations in the same
mathematical patterns, but one set is used
to determine linear quantities while one
set is used to determine rotational
quantities, or those that go in a circle.
20. From page 225, do problems 1, 5, 7, 17, 19, and 20.
1. A diver completes 3 ½ somersaults in 1.7 seconds. What is the average angular speed (in rad/s) of the
diver?

  3.5 rev  2 rad 


  13 rad/s
t  1.7 s  1 rev 
5. A CD has a playing time of 74 minutes. When the music starts, the CD is rotating at an angular speed of 480
revolutions per minute (rpm). At the end of the music, the CD is rotating at 210 rmp. Find the magnitude of the
average angular acceleration of the CD (in rad/s2).
2
  210 rev/ min  480 rev/ min  2 rad  1 min 
3
2




  – 6.4  10 rad/s
t 
74 min
  1 rev  60 s 
7. An electric circular saw is designed to reach its final angular speed, starting from rest, in 1.5 seconds. Its
average angular acceleration is 328 rad/s2. Obtain its final angular speed.
  0   t  0 rad/s  (328 rad/s2 )(1.50 s)  492 rad/s
17. An electric fan is running on HIGH. After the LOW button is pressed, the angular speed of the fan
decreases from 83.8 rad/s in 1.75 s. The deceleration is 42.0 rad/s2. Determine the initial angular speed of the
fan.
0     t  83.8 rad/s – (–42.0 rad/s2 )(1.75 s) = 157.3 rad/s
19. A flywheel has a constant angular deceleration of 2.0 rad/s2. If the flywheel comes to a rest from an
angular speed of 220 rad/s, find:
a. The angle through which the rotor turns.
 2  02  0 rad/s   (220 rad/s) 2
4


 1.2  10 rad
2
2
2(–2.0 rad/s )
2
b. The time required for the flywheel to come to rest.
  0 0 rad/s  220 rad/s
t

 1.1 102 s
2

–2.0 rad/s
20. The angular speed of the rotor in a centrifuge increases from 420 to 1420 rad/ s in a time of 5 seconds.
c. Find the angle through which the rotor turns
 = 12 ( + 0 ) t = 12 (1420 rad/s + 420 rad/s)(5.00 s) = 4.60  103 rad
d. Find the magnitude of angular acceleration
  0
1420 rad/s  420 rad/s
=
=
= 2.00  102 rad / s2
t
5.00 s