Chapter 10 &11 Rotational motion about a Fixed Axis Torque, Rotational Inertia and Law Work and Rotational Kinetic Energy Angular Momentum and Conservation of Angular Momentum
Chapter 10 & 11 Rotational Motion About a Fixed Axis • Torque, Rotational Inertia and Law • Work and Rotational Kinetic Energy • Angular Momentum and Conservation of Angular Momentum
1. Angular Quantities( P235-238 Angular position 0 2 Angular displacement(角位移):△6=62-61 Where ae is positive for counterclockwise rotation and negative for clockwise rotation Always:0=6t △ede 3.Angular velocity: @=lim 4→+0△tdt 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
1. Angular Quantities (P235-238) 1.Angular position : 2.Angular Displacement(角位移): Where is positive for counterclockwise rotation and negative for clockwise rotation. Always: = (t) = 2 −1 t t t d d lim 0 = = → 3.Angular Velocity : 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)
4.Angular Acceleration △ada a= m A→>0△tdt
t t t d d lim 0 = = → 4.Angular Acceleration :
2. Relation of Linear and Angular Variables The distance along a circular arc S=Or (radian me as ure ) The linear speed (with r held constant): ds de or 一[V=o〃 dt dt The tangential component at: a =ar The radial component an 2
r dt d dt ds = v=r or 2. Relation of Linear and Angular Variables The distance along a circular arc: The linear speed (with r held constant): s = r (radian measure). The tangential component at : r t = The radial component an : 2 2 v r r v an = = =
3. Kinematics Equations for Uniformly Accelerated Rotational Motion(p238) Equations of Motion for Constant Linear Acceleration are analogous to the ones of Constant Angular acceleration Linear Missing Angular Equation variable Equation y=vo t at X 0=0+at x-xo=lot t-ai 6-6 Oot ta at 2 12=v2+2c(x-x0) 02=02+2a(-t C -6=(0o+0) X-x 0=v 2 6-0.=0t2q
- 0 = 0 +t - 0 = 0 t + t 2 t 2 = 0 2 +2( -0 ) - 0 = (0 + )t 0 - 0 = t - t 2 v = v0 + at x -x0 x - x0 = v0 t + at2 v v 2 = v0 2 + 2a(x - x0 ) t x - x0 = (v0 + v)t a x - x0 = vt - at2 v0 Equations of Motion for Constant Linear Acceleration are analogous to the ones of Constant Angular Acceleration: Linear Missing Angular Equation variable Equation 2 1 2 1 2 1 2 1 2 1 2 1 3. Kinematics Equations for Uniformly Accelerated Rotational Motion(p238)