文档介绍：Rotation of Rigid Bodies
Angular Motion
Angular Motion Definitions
Rotational kinematics: describes rotational motion.
Rigid body: idealized model of a body which has a perfectly definite and unchanging shape and size.
Rigid Bodies
A rigid body is one where all the
particles maintain their
relative position
As the body rotates
Each particle moves
Relative positions don’t change
Bowling Green
Sydney
Cities on the earth are always moving
But they don’t get closer together
Angular Motion Definitions
First, let’s discuss the rotation of rigid body about a fixed axis.
Fixed axes: axes which is at rest in some inertial frame of reference and does not change direction relative to that frame.
We will usually select the origin of our x-y plane to be in the same as the plane that the rotating object occupies and the origin O corresponded to the location of the axis of rotation.
Then, if we pick a point on the rotating object and draw a line from this point to the origin it will make an angle q with the x-axis. This angle is called the angular position.
The angular displacement will be defined as a change in angular position, Dq = q2 - q1, during a time interval Dt = t2 - t1.
Both angular position and angular displacement will most commonly be expressed in radians. To convert between radians, revolutions, and degrees use the conversion:
1 revolution = 2 p radians = 360 degrees
Angular Motion Definitions
One radian is the angle subtended at the center of a circle by an arc with a length equal to the radius of this circle.
Angle θ is subtended by an arc with a length S equal on a circle of the radius r.
Angle in radians is the ratio of two lengths, so it is a pure number (NO dimensions).
Angular Motion Definitions
The average angular velocity wav-z is the angular displacement per unit time
The instantaneous angular velocity wz is the limit of wav-z when Dt approaches zero. This is derivative of angular position with respect to time.