84.5 The circular motion 2. How to describe the circular motion? ANgular position( coordinate )(d i y,v 2 Angular displacement 40(r) Are length As=r48 speed and position of the particle ds(t) v m dta→0st r(t=x(t)i +y(t)j lim r40 d8(t) rcos 6+rsin 4→+0s 84.5 The circular motion @angular speed and angular velocity vector Right-hand rule for k Define: the time rate of ar=a( k change of the angular coordinate of the particle is the angular 6 speed de(r m(= angular velocity vector o(()=a(rk=do( 1414 §4.5 The circular motion 2. How to describe the circular motion? r i r j r t x t i y t j ˆ sin ˆ cos ˆ ( ) ˆ ( ) ( ) = θ + θ = + r t t r t r t s t s t v t t d d ( ) lim lim d d ( ) 0s 0s θ ∆ ∆θ ∆ ∆ ∆ ∆ = = = = → → 1Angular position (coordinate)θ (t) 3speed and position of the particle 2 Angular displacement∆θ (t) Arc length ∆s = r∆θ v r v r ∆θ r r θ x y §4.5 The circular motion 4angular speed and angular velocity vector Right-hand rule for k ˆ Define: the time rate of change of the angular coordinate of the particle is the angular speed t t t z d d ( ) ( ) θ ω = r r θ x y z t t k z ˆ ω( )=ω ( ) r v r k t t t z t k ˆ d d ( ) ˆ ( ) ( ) θ ω =ω = r angular velocity vector