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⊥