Physics, 3 Edition

copygrouperΜηχανική

13 Νοε 2013 (πριν από 4 χρόνια και 1 μήνα)

92 εμφανίσεις

© 2007 Pearson Prentice Hall

This work is protected by United States copyright laws and is provided solely for
the use of instructors in teaching their courses and assessing student learning.
Dissemination or sale of any part of this work (including on the World Wide Web)
will destroy the integrity of the work and is not permitted. The work and materials
from it should never be made available to students except by instructors using
the accompanying text in their classes. All recipients of this work are expected to
abide by these restrictions and to honor the intended pedagogical purposes and
the needs of other instructors who rely on these materials.

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.