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 2 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 . From degrees to radians we use . From revolutions to radians we use . From radians to revolutions we use . From revolutions to degrees we use . From degrees to revolutions, we use .

  1. What are the positive and negative conventions for rotational motion? positive is counter-clockwise motion while negative is clockwise motion.
  2. Copy figure 8.3 with the explanation of the radian measurement.
  1. 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
  2. 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
  3. What is the symbol for angular velocity? ω omega, the Greek symbol
  4. What is the equation for angular velocity?

average angular velocity = = =

  1. What are the units for angular velocity?rad/s
  2. Copy example 3 “Gymnast on a High Bar” example into your notebooks.
  3. What is instantaneous angular velocity? Instantaneous angular velocity is the angular velocity that exists at any given instant.
  4. What is the symbol for angular acceleration? α omega, the Greek symbol
  5. What is the equation for angular velocity?

average angular acceleration = = =

  1. What are the units for angular acceleration? rad/s2
  2. Copy example 4 “A jet Revving Its Engines” into your notebooks.
  3. Copy table 8.1 “The Equations of Kinematics for Rotational and Linear Motion” into your notebook. Compare and contrast the equations.

  1. 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?

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).

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.

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.

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:

  1. The angle through which the rotor turns.
  1. The time required for the flywheel to come to rest.

20. The angular speed of the rotor in a centrifuge increases from 420 to 1420 rad/ s in a time of 5 seconds.

  1. Find the angle through which the rotor turns

=

  1. Find the magnitude of angular acceleration

=