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Lecture Outlines
Chapter 10
Physics, 3
rd
Edition
James S. Walker
Chapter 10
Rotational Kinematics and
Energy
Units of Chapter 10
•
Angular Position, Velocity, and
Acceleration
•
Rotational Kinematics
•
Connections Between Linear and
Rotational Quantities
•
Rolling Motion
•
Rotational Kinetic Energy and the
Moment of Inertia
•
Conservation of Energy
10

1 Angular Position, Velocity, and
Acceleration
10

1 Angular Position, Velocity, and
Acceleration
Degrees and revolutions:
10

1 Angular Position, Velocity, and
Acceleration
Arc length
s
,
measured in
radians:
10

1 Angular Position, Velocity, and
Acceleration
10

1 Angular Position, Velocity, and
Acceleration
10

1 Angular Position, Velocity, and
Acceleration
10

1 Angular Position, Velocity, and
Acceleration
10

2 Rotational Kinematics
If the angular
acceleration is
constant:
10

2 Rotational Kinematics
Analogies between linear and rotational
kinematics:
10

3 Connections Between Linear and
Rotational Quantities
10

3 Connections Between Linear and
Rotational Quantities
10

3 Connections Between Linear and
Rotational Quantities
10

3 Connections Between Linear and
Rotational Quantities
This merry

go

round
has both tangential and
centripetal
acceleration.
10

4 Rolling Motion
If a round object rolls without slipping, there
is a fixed relationship between the
translational and rotational speeds:
10

4 Rolling Motion
We may also consider rolling motion to be a
combination of pure rotational and pure
translational motion:
10

5 Rotational Kinetic Energy and the
Moment of Inertia
For this mass,
10

5 Rotational Kinetic Energy and the
Moment of Inertia
We can also write the kinetic energy as
Where
I
, the moment of inertia, is given by
10

5 Rotational Kinetic Energy and the
Moment of Inertia
Moments of inertia of various regular objects can
be calculated:
10

6 Conservation of Energy
The total kinetic energy of a rolling object is the
sum of its linear and rotational kinetic energies:
The second equation makes it clear that the
kinetic energy of a rolling object is a multiple of
the kinetic energy of translation.
10

6 Conservation of Energy
If these two objects, of the same mass
and radius, are released
simultaneously, the disk will reach the
bottom first
–
more of its gravitational
potential energy becomes translational
kinetic energy, and less rotational.
Summary of Chapter 10
•
Describing rotational motion requires analogs
to position, velocity, and acceleration
•
Average and instantaneous angular velocity:
•
Average and instantaneous angular
acceleration:
Summary of Chapter 10
•
Period:
•
Counterclockwise rotations are positive,
clockwise negative
•
Linear and angular quantities:
Summary of Chapter 10
•
Linear and angular equations of motion:
Tangential speed:
Centripetal acceleration:
Tangential acceleration:
Summary of Chapter 10
•
Rolling motion:
•
Kinetic energy of rotation:
•
Moment of inertia:
•
Kinetic energy of an object rolling without
slipping:
•
When solving problems involving conservation of
energy, both the rotational and linear kinetic
energy must be taken into account.
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