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Chapter 11 ROTATION
11.1 The Motion of Rigid Bodies
11.1.1 Rigid bodies
A rigid body is defined as a body of which
the distance between any two particles is not
changed.
This is another ideal model for dealing with
physical problems.
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11.1.2 The classification of the motion of rigid
bodies
(i) Translational motion The motion in which
any straight line in a rigid body is always
parallel
(ii) Rotation about a fixed axis The motion in
which any particle in a body is in a circular
motion of a radius about an identical straight
line keeping constant position
(iii) Rotation about a fixed point
(iv) A planar motion of a rigid body The motion
in which any particle in the body is always in
its plane
(v) A general motion of a rigid body.
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11.2 Angular Kinematics
12.2.1 Rotation about a fixed axis
In a rotation about a fixed axis, any
particle in the body turns the same angle as
others though the distance to the axis may be
different. Therefore, we can chose an angular
coordinate to represent the position of the rigid
body.
Angular displacement
Average angular velocity
Instantaneous angular velocity
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Average angular acceleration
Instantaneous angular acceleration
On the other hand, with some initial
conditions, angular equation can be solved
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11.2.2 Relation of linear and angular quantities
The relationship between linear and angular
quantities
Further definition of angular velocity vector
And angular acceleration vector
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Thus,
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11.3 Kinetic Energy of Rotation
11.3.1 Kinetic energy of rotation
The kinetic energy of a rigid body is
Rotational inertia
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11.3.2 Calculating the rotational inertia
For a collection of point masses
For continuously distributed mass
It is related to the mass distribution about an
axis.
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Parallel-axis theorem
Normal-axis theorem
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11.4 Newtons Second Law in Angular Form
11.4.1 Torque
Generally, torque is defined as
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The torque of a force about a axis is the
component of the torque about a point on the axis.
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11.4.2 Newtons second law for rotation
We consider the simple situation
The torque
Generally, we have
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11.4.2 Newtons second law for rotation
We consider the simple situation
The torque
Generally, we have
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From the rotation law
We get the work-kinetic energy theorem for
rotation
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If the force acting on the body is conservative,
then we have
The conservation of mechanical energy in
rotational motion
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Problems

1. 11-4 (on page 239),
2. 11-25,
3. 11-37,
4. 11-38,
5. 11-57,
6. 11-66.

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