Question

HINT: this problem is about using different coordinate systems to solve kinematics problems! D 4. As rod OA rotates, pin P moves along the curve BCD with a constant speed of 3 m/s (in the counterclockwise direction). The equation for this curve is r = 2/(1+cose). Solve the following for the point shown, when 0 = 1/6 (radians). 0 1m B a) Find dr/dt and do/dt, and express the velocity vector in polar coordinates. b) Find the polar unit vectors e, and ea, in terms of i and j. Use what you know about the velocity to find the normal and tangential (path) unit vectors (et and e) in terms of i and j, and in terms of e, and eg. c) Express the acceleration in path coordinates and use this information to calculate d?r/dt? and d0/dt?, and express the acceleration in polar coordinates. d) Express the velocity and acceleration in Cartesian coordinates

Answer 1

0 Ano Giren that, equation is The i 91: 2 vi (i+Coso) at O=1716 NE 2 1+60[77] 91:1.072m. છે . આ dt : 2 d dt [hicosod] = 2 (1) (l+cooost (-sino) do at ممنو2 It coses der dt dr dt = Vor 2 zsin3o It cosso? é < 0.2870 Abo, V=r RO Quora :1107206 Nowy Whet - (103 + CW5715 23.

3. 00720)+(0.2376) ..9=27 hadds Now Vo = der dt -0.2870. 2 0.287X24 Vor=0.775 4 Vo =liorzo. CA 22.9 co m/s - Vo C r b) od=0AHÁC rég = cosoita sinoi Cosoit sings Pinilarly for io OB = A + B GO (TTINUM So, fo = Esine) i Hcosoj. Mas Velocilā depends on (01,0). dr تلك ar ao Әя де + Ərdo St (By total differentiation famulan). dr dt cão = Vor av ar of Vo ge de A10 n1 radial - ¿no Azso Noiz ce coill fina ģi fust: 2 Sino .o (l+coso) À der dt no

Šia el sino (1+cosos o] con el 2 Sino 14 Cooo? بل 2sino (1+Cosor co). de gi - 0 hos] to. at ós 2oBAC1+C0503-2C1+COSO)C-Sino) (1+Cosa)n)? Here Becona dém becomes pero since Q :0. B (O) = 0 ca. girdo du- Jo 2008 30C1+C88303 +2614C0330) Csino (+C8830)4 9 : ex (0.5) 2 (2=500165). ģi= 4,75 m/s So aradial 2 di-ro 24175-(1072) (217 Gradial :-306488ên a tangential snö +2 gie Here ó:d0. alärgential + 2x sixe - 2x07758X 2.4. =4.19 io mls. tang Vnet 23m/s A d) Lace ve 2 Vor 2.9 07758 75.02 149 22 10-18 Be75.02 10:20

so Vez - het cos(74.98), ke= -3 cos 74.98 c-017775 mls. Vy Vret (Sin 74,98). Vy - 3sin (74198) Vy e 2.8915mls art -3.06488în fri 9 28 Oo -4:19 S larap ar ao aor 4.19 m/s² 306488 4.999 I 01 IB 360 ß = 36:18 000 -> anet (cars+cool anet z Siams Tonet az-a net Cos(26-13). an sin ( 20.pl a-Sizcos (120°-36118) 23120-2) 60 984 anet Cos(120- B. 120-3). ana 0.56 mis 130 Ay = -anet sin (120°-P) 1-5.25in120-36:18) -5,17 ay: -5.17 mls.