Chapter
8
Rotational Motion
In this chapter you will:
Learn how to describe and
measure rotational motion.
Learn how torque changes
rotational velocity.
Define center of mass and
the conditions for
equilibrium.
Chapter
Table of Contents
8
Chapter 8: Rotational Motion
Section 8.1: Describing Rotational Motion
Section 8.2: Rotational Dynamics
Section 8.3: Equilibrium
Assignments:
Read Chapter 8.
Study Guide 8 due before the Chapter Test.
HW 8.A: p.223: 72-77.
HW 8.B: p.224: 81,82,84. p.225: 91,97.
HW 8.C: Handout
Section
8.1
Describing Rotational Motion
In this section you will:
Describe angular displacement.
Calculate angular velocity.
Calculate angular acceleration.
Solve problems involving rotational motion.
Section
8.1
Describing Rotational Motion
Describing Rotational Motion
Length = d
A fraction of one revolution
can be measured in grads,
degrees, or radians.
A grad is 1/400 of a revolution.
A degree is 1/360 of a revolution.
The ___________________ is defined as ½ π of a revolution.
The abbreviation of radian is ‘rad’. The distance around the circle
is 2πr.
One complete revolution is equal to 2π radians, so
360 degrees = 2 π radians
Section
8.1
Angular Displacement
The Greek letter theta, θ,
is used to represent the
angle of revolution.
The counterclockwise
rotation is designated
as positive, while
clockwise is negative.
As an object rotates, the
change in the angle is
called_______________
For rotation through an angle, θ, a point at a distance, r, from the
center moves a distance given by _________________________.
Section
8.1
Describing Rotational Motion
Angular Velocity
Velocity is displacement divided by the time taken to make the
displacement.
The
of an object is angular
displacement divided by the time required to make the displacement.
The angular velocity of an object is given by:
Here angular velocity is represented by the Greek letter omega, ω.
The angular velocity is equal to the angular displacement divided by
the time required to make the rotation.
Section
8.1
Describing Rotational Motion
Angular Velocity
For Earth, ωE = (2π rad)/(24.0 h)(3600 s/h) = 7.27×10─5 rad/s.
In the same way that counterclockwise rotation produces positive
angular displacement, it also results in positive angular velocity.
If an object’s angular velocity is ω, then the linear velocity of a point a
distance, r, from the axis of rotation is given by
The speed at which an object on Earth’s equator moves as a result of
Earth’s rotation is given by
v = r ω = (6.38×106 m) (7.27×10─5 rad/s) = 464 m/s.
Earth is an example of a rotating, rigid object. Even though different
points on Earth rotate different distances in each revolution, all points
rotate through the same angle.
Section
8.1
Describing Rotational Motion
Angular Acceleration
is defined as the change in angular
velocity divided by the time required to make that change.
The angular acceleration, α, is represented by the following
equation:
Angular acceleration is measured in
If the change in angular velocity is positive, then the angular
acceleration also is positive.
.
Section
8.1
Describing Rotational Motion
Angular Acceleration
A summary of linear and angular relationships.
p.200: Practice Problems: 1,2. Section Review: 5,7-10.
HW 8.A: p.223: 72-77.
Section
Section Check
8.1
Question 1
What is the angular velocity of the minute hand of a clock?
A.
B.
C.
D.
Section
Section Check
8.1
Question 2
When a machine is switched on, the angular velocity of the motor
increases by 10 rad/s for the first 10 seconds before it starts rotating
with full speed. What is the angular acceleration of the machine in
the first 10 seconds?
A.
π rad/s2
B.
1 rad/s2
C.
100π rad/s2
D.
100 rad/s2
Section
Section Check
8.1
Question 3
When a fan performing 10 revolutions per second is switched off, it
comes to rest after 10 seconds. Calculate the average angular
acceleration of the fan after it was switched off.
A.
1 rad/s2
B.
2π rad/s2
C.
π rad/s2
D.
10 rad/s2