物理与光电工程学院：《大学物理》课程PPT教学课件（讲稿，英文第三版）Chapter 10&11 Rotational Motion

Chapter 10&ll 质点的转动 Chapter 10 &e 11 Rotational motion Angular Quantities Torque Angular Momentum Conservation of Angular Momentum

Chapter 10&11 质点的转动 Chapter 10 & 11 Rotational Motion • Angular Quantities • Torque • Angular Momentum • Conservation of Angular Momentum

Chapter 10&ll 质点的转动 10-1.Angular Quantities(P235-237) 1.Angular position 0 p235: We measure the angular position 6 of this line relative to a fixed direction (x) △s △0 Unit of: radian(rad)弧度 0

Chapter 10&11 质点的转动 10-1. Angular Quantities (P235-237) r s  = Unit of : radian( rad) 弧度    o r s x s We measure the angular position  of this line relative to a fixed direction (x). 1.Angular position  p235:

Chapter 10&ll 质点的转动 2. Angular Displacement(角位移):△ a body that rotates about a rotation axis, changing its angular position from 6, to 62, undergoes an angular displacement: △b=6,-01 Where△ e is positive for counterclockwise(逆时 针) rotation and negative for clockwise.(顺时针) rotation Always: 6=60

Chapter 10&11 质点的转动 2.Angular Displacement(角位移):  ●Where  is positive for counterclockwise（逆时 针） rotation and negative for clockwise（顺时针） rotation. Always:  = (t) a body that rotates about a rotation axis, changing its angular position from 1 to 2 , undergoes an angular displacement:  = 2 −1

Chapter 10&ll 质点的转动 3.Angular velocity p236: P(△n △bd6 0= lim Q△ 4→>0△tdt The magnitude of the bodys angular velocity is the angular speed. 方向:满足右手定则,沿刚体转动方向右旋大拇指指 Right-hand-rule: When the fingers of the right hand are curled around the rotation axis and point in the direction of the rotation, then the thumb points in the direction of

Chapter 10&11 质点的转动  x y o  P(t) P0 r  t t t d d lim 0    =   =  → 3.Angular Velocity p236: The magnitude of the body’s angular velocity is the angular speed. 方向：满足右手定则，沿刚体转动方向右旋大拇指指 向。 Right-hand-rule: When the fingers of the right hand are curled around the rotation axis and point in the direction of the rotation, then the thumb points in the direction of . (p241) 

Chapter 10&ll 质点的转动 4.Angular Acceleration 237 TThe limit of the ratio as time interval approaches zero. △od a=m 4→0△tdt

Chapter 10&11 质点的转动 t t t d d lim 0    =   =  → 4.Angular Acceleration p237: The limit of the ratio as time interval approaches zero

Chapter 10&ll 质点的转动 5. Relation of Linear and Angular Variables p237 The distance along a circular arc s=8r (radian me as ure). The linear speed(with r held constant) ds de or 「v=or dt dt Differentiating above equation with respect to time(ragain holds constant) dt dt

Chapter 10&11 质点的转动 r dt d dt ds  = v=r or 5. Relation of Linear and Angular Variables p237 The distance along a circular arc: Differentiating above equation with respect to time (r again holds constant) r dt d dt dv  = The linear speed (with r held constant): s = r (radian measure)

Chapter 10&ll 质点的转动 The tangential component a c,= The radial component an

Chapter 10&11 质点的转动 The tangential component at : r t = The radial component an : 2 2 v r r v an = = =

Chapter 10&ll 质点的转动 7=7Ce t a=rae troe Example 10-2 page 238

Chapter 10&11 质点的转动 et r   v =    r  t e  v  2 n t   a r a r = = t a  n a  n 2 t a r e r e    =  +  a  Example 10-2 page 238

Chapter 10&ll 质点的转动 10-2. Kinematics Equations for Uniformly Accelerated Rotational Motion(p238) Equations of Motion for Constant Linear Acceleration are analogous to the ones of Constant Angular Acceleration 质点匀变速直线运动绕定轴作匀变速转动 7=00+Ct 0=0+at x=xo +vot+iate=0+ot+l at 72=b+2a(x-x)a32=a2+2a(6-6)

Chapter 10&11 质点的转动 10-2. Kinematics Equations for Uniformly Accelerated Rotational Motion(p238) Equations of Motion for Constant Linear Acceleration are analogous to the ones of Constant Angular Acceleration: 质点匀变速直线运动 绕定轴作匀变速转动 = + at v v0 2 2 1 x = x0 + v0 t + at 2 ( ) 0 2 0 2 v = v + a x − x  = +t 0 2 ( ) 0 2 0 2  = +   − 2 2 1 0 0  = + t + t

Chapter 10&ll 质点的转动 11-3 Angular Momentum of a particle(P277-278) 1. Torque on an axis(对轴的力矩) The torque about a given axis is defined as z=R1F=RF⊥ or t=REsin where r, is called moment arm- the distance from the axis of rotation Point of Axis of application that is perpendicular to the rotation of force R line of action of the force Its si units: m N R

Chapter 10&11 质点的转动 1. Torque on an axis (对轴的力矩) : 11-3 Angular Momentum of a particle (P277-278)  = RF sin where is called r⊥ moment arm —— the distance  = R⊥ F Its SI units: m N The torque about a given axis is defined as: or from the axis of rotation that is perpendicular to the line of action of the force. = RF⊥