84.5 The circular motion 3. Nonuniform circular motion nd the angular acceleration ① angular acceleration (t)= la(t)xr(t) do(t) 、do() r(t)+() ) a(t) dt dt =a(t)×r(t)+o(t)×v(t) a2()k Angular acceleration centripetal acceleration 84.5 The circular motion 2 The direction of angular acceleration Speeding up: a(t) is parallel to@(t) Slowing down: a(t)is antiparallel to @(t) Tangential acceleration a(t=a(txr(t)+o(t)xv(t) rat+ovn= rt+—n 1616 §4.5 The circular motion 3. Nonuniform circular motion and the angular acceleration ( ) ( ) ( ) ( ) d d ( ) ( ) ( ) d d ( ) [ ( ) ( )] d d d d ( ) ( ) t r t t v t t r t r t t t t t r t t t v t a t r r r r r r r r r r r r = × + × = × + × = = × α ω ω ω ω Angular acceleration centripetal acceleration 1 angular acceleration t k t t t z ˆ ( ) d d ( ) ( ) α ω α = = r r ω r α r z n r v rt dt d r t vn a t t r t t v t z ˆ ˆ ˆ ˆ ( ) ( ) ( ) ( ) ( ) 2 = + = + = × + × ω α ω α ω r r r r r 3tangential acceleration §4.5 The circular motion 2 The direction of angular acceleration ω r ω r α r α r Speeding up: is parallel to . Slowing down: is antiparallel to . α(t) r ω(t) r α(t) r ω(t) r