Chapter 8 Rotational kinematics A
Chapter 8 Rotational kinematics
Section 8-1 Rotational motion The general motion of a rigid object will include both rotational and translational components For example The motion of a wheel on a moving bicycle A wobbling football in flight is more complex case Rotations with only one fixed point Rotations (定点转动) Rotations with fixed axis(定轴转动) pure rotation
Section 8-1 Rotational motion The general motion of a rigid object will include both rotational and translational components. For example: The motion of a wheel on a moving bicycle; A wobbling football in flight is more complex case. Rotations Rotations with fixed axis(定轴转动) Rotations with only one fixed point （定点转动） pure rotation
Two definitions of a pure rotation a Every point of the body moves in a circular path. The centers of these circles must ie on a common straight line called the axis of rotation B 口 Any reference line A perpendicular to the axis (such as AB in Fig 8-1) moves through the same angle in a given time interval
Every point of the body moves in a circular path. The centers of these circles must lie on a common 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:
How many freedoms are needed to describe completely for a pure rotation? 1(R How many for a rotation with only one fixed point? 3 (R 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
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 describe completely for a pure rotation? 1(R) How many for a rotation with only one fixed point? 3(R)
8-2 The rotational variables 1. Angular displacement Fig 8-4 shows a rod rotating about the z axis. Any point p on the od will trace an arc of a circle A The angle o is the angular position of the reference line ap with y A respect to the x axis. x g
2 2 ,t 1 ,t 1 P1 P2 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 A P x y 1. Angular displacement