# Physics, 3 Edition

Mechanics

Nov 13, 2013 (4 years and 8 months ago)

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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

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
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.