Rotation of rigid body about

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Chapter 5 Rotation of rigid body about fixed axis
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Key words
??Rigid body ??Rotation ??translation ??
fixed axis ??fixed point ???Angular
velocity ????Angular acceleration
????Kinetic energy in rotation ?Work
??Power
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Key words
????Moment of inertia ???system of
particles ??torque
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Rigid bodyshape and size will never change (
idealized model )
directions
1. Rigid body is a special system of particles
,the distance between any two particles will not
change .
2. All rules of system of particles can be
applied to rigid body with a simpler form
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• 5.1 motion of rigid body

?. motion of rigid body
translation 1.all points of the rigid body
have parallel orbit ?
2.The line connecting any two points of the rigid
body remains parallel in motion
3.The global motion of the body can be
represented by any point(eg. Center of the mass)
rotation
?rotation about a fixed axis
?rotation about a fixed point
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?rotation about a fixed axis
Axis motionless points of the rigid
body. Direction along the angular velocity
o'

relative motion of two points of the rigid body
can only be realized by rotation
o
?rotation about a fixed point
Only one point on the rigid body will remain
motionless ,the axis keeps changing
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3.typical motion
Motion without limitation
Combination of Translation and rotation
The motion of the earth around the sun
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??angular description of rotation
Its relation with the axis?
Rotational plane
Uniformity All particles are rotating about the
same axis
Uniformity in the rotation though with various
radius,all points have the same angular velocity
Which is the direction of Angular momentum of the
particles?
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1.angular terms in rotation
Angular displacement
??
Angular v
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?
The direction of the axis and the rapidity of
the rotation
The vector of angular v
?
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1.angular terms in rotation
Angular displacement
??
Angular v
Angular acceleration
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2.rotation about a fixed axis
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Translation and rotation
In translation ,force produce acceleration
m measures the inertia in translation
In rotation, torque produce angular acceleration
J measures the inertia in rotation
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Kinetic energy and velocity
Translation Kinetic energy and velocity
Rotation kinetic energy and angular velocity
J moment of inertia
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• 5.2 rotational kinetic energy and moment of
  inertia

----system of particles
1. kinetic energy in rotation
1?cut the rigid body into numerous particles ,the
kinetic energy of the piece with mass of ?mi
2.kinetic energy of the rigid body
r is the distance from the axis
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• moment of inertia

• definition
• (to the axis)

dimension kgm2

• calculation

For rigid body with continuous mass
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Continuous mass distribution
m
Linear density
L
m
s
Body density
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Popular J
ring
disk
stick
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• 5.3 toque theorem of rotation

??torque (to the axis) 1. Force
locating in the rotational plane
The center of the circle of any particle is on
the axis
Torque contributing to the rotation
Applying a torque along an axis results in
rotation about the axis
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Force locating outside the rotational plane
The parallel part can deform the axis but will
not result in rotation.
without further notation,given torque is
usually along the axis
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Theorem of rotation
Angular momentum along the axis
For all rotating particles
O
Rigid body
z
Momentum of inertia along z
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O
Rigid body
z
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Angular momentum along z
Torque along z
For any fixed axis
Theorem of rotation
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Theorem of rotation
Forum
1. With constant M ,
Moment of inertia measures inertia
2.the sign of M define a positive direction
Along the axis is positive Opposite is negative
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Eg.1.? calculate
ß.
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(No Transcript)
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Eg.2. After time t the block hits the board
,calculate the moment of inertia?
(1)
m g
(2)
T
a
R
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M g
(1)
(2)
(4)
(3)
(1)(4)
analysis
1. h and m given , the bigger the momentum of
inertia the longer the time
2. When the momentum of inertia is zero or
neglected, we get a free falling body.
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• 5.4 work of the torque

dW
For a process
Accumulation of torque over space
power
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2.Kinetic energy in rotation
Work by the torque the incensement of the
rotational kinetic energy
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homework
Chapter 5 1, 2, 4
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5.1 ????????????????m1?m2???,???????r
,???m???,?????????????
5.4 ???m,??l??????????????,??????????????,?????30?
??? 1? ???????,??????? 2 ????,?????????
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5.2 ?????60??,??0.25?, ???900?/??,???????????f,???
?????????0.4? 1?????100?,???????????,?????????? 2.
?????????????,??????
f
0.5
0.75