axis(定轴转动).ppt

文档介绍：Chapter 8 Rotational kinematics
Section 8-1 Rotational motion
The general motion of a rigid object will include both rotational and ponents.
For example:
The motion of a wheel on a moving bicycle;
A wobbling football in flight is plex case.
Rotations
Rotations with fixed axis(定轴转动)
Rotations with only one fixed point
(定点转动)
pure rotation
Every point of the body moves in a circular path. The centers of these circles must lie on mon straight line called the axis of rotation.
Any reference line perpendicular to the axis (such as AB in Fig 8-1) moves through the same angle in a given time interval.
x
y
z
B
A
Fig 8-1
p
Two definitions of a pure rotation:
In general the three-dimensional description of a rigid body requires six coordinates: three to locate the center of mass, two angles (such as latitude and longitude) to orient the axis of rotation, and one angle to describe rotations about the axis.
How many freedoms are needed to pletely for a pure rotation?
1(R)
How many for a rotation with only one fixed point?
3(R)
A
x
y
Fig 8-4
8-2 The rotational variables
Fig 8-4 shows a rod rotating about the z axis. Any point P on the rod will trace an arc of a circle.
The angle is the angular position of the reference line AP with respect to the x axis.
Z
P
A
x
y
1. Angular displacement
We choose the positive sense of the rotation to be counterclockwise(逆时针).
(8-1)
where the s is the arc which the point P moves, and r is the radius (AP).
At time the angular position is , at is . The angular displacement of P is during
.
We define the average angular velocity as
(8-2)
The instantaneous angular velocity is
(8-3)
Is a vector quantity?
2. Angular velocity
The dimensions of inverse time ( ); its units may be radians per second ( ) or revolutions per second ( ).
If the angular velocity of P is not constant, then the average angular acceleration is defined as
(8-4)
The instantaneous angular acceleration is
(8-5)
3. Angular