华南农业大学物理力学（英文版）：《 MECHANICS》

③革由接掌大孝 但博学一求宣倒新 South chi na Agricul tural Uni versity 3. Discussion of curve motion Projectile motion O The velocity of particle is dx VocodE d t y vo sin 8o-gt 6 2 The displacement of particle is dt cos dt=vcos 0 . y=v, dt= (vo sin 8o-gt)dt =vo sin 8oot-gt

D e p. p h y sic s D e p. p h y sic s D e p. p h y sic s 11 3. Discussion of curve motion • Projectile motion ① The velocity of particle is: ② The displacement of particle is: 0 0 0 0 c o s s i n x y d x v v d t d y v v g t d t        0 0 0 0 0 0 2 0 0 0 0 0 0 cos cos 1 ( sin ) sin 2 t t x t t y x v dt v dt v t y v dt v gt dt v t gt                   0 v 0 x y

革擦大寧 但博学求回新 South chi na Agricul tural Uni versity · Circular motion (1) the rotational variables ① angular velocity d e △t→0△t d t 2 angular acceleration B=1 Im △t→>0 d t d t 12

Dep. physics Dep. physics Dep. physics 12 • Circular motion (1) the rotational variables ① angular velocity ② angular acceleration 0 l i mt t d t d t           2 2 0 li mt t d d t d t d t            

革擦大寧 但博学求回新 South chi na Agricul tural Uni versity (2)relationship between linear and angular variables △l=R△O △ 6 Im = Rlim R △t→)0 △ △t R R R R B d t d t 13

D e p. p h y sic s D e p. p h y sic s D e p. p h y sic s 13 (2)relationship between linear and angular variables 0 0 2 2 lim lim t t n t l v R R t t v a R R d v d a R R d t d t                      l  R o R  l

革擦大寧 South chi na Agricul tural Uni versity 佰德博学一创新 (3 Uniform circular motion B R O A limit △6→>0 Direction of acceleration normal △V △V A replacing R B Magnitude of acceleration △ lim - Centripetal acceleration) △→>0△tR△1→>0△tR

D e p. p h y sic s D e p. p h y sic s D e p. p h y sic s 14 (3) Uniform circular motion A limit:   0  Direction of acceleration: normal A replacing: l v R v     Magnitude of acceleration: l  o R  A v  B v  v   A v  B v  o  2 0 0 n lim lim t t v v l v a  t R  t R          (Centripetal acceleration)

③革由接掌大孝 South chi na Agricul tural Uni versity 佰德博学一求创新 (t+△t) (4)Variable circular motion v(1) △V Ac d=1im二 =1im一+liCB APR t→>0 △ △ △ Ac R △ B CB v(t) Im m △ 1→>0△t1→>0△tat v(t+△) 15

D e p. p h y sic s D e p. p h y sic s D e p. p h y sic s 15 (4) Variable circular motion C A B v (t)  v   v(t  t)   o  x v (t)  s  O R v(t  t)  0 0 0 lim lim lim t t t v AC CB a  t  t  t             2 0 lim n t AC v a  t R      0 0 lim lim t t CB v dv a t t dt            