Question

QUESTION 3 a) With a simple schematic diagram, explain why rolling motion is considered as general plane motion. Explain also why we need to assume that there is no slipping occurs during rolling motion in kinematics analysis of rolling object. [CO1/P01/C2] (5 marks) b) Pin B is welded to the disk and freely slides within the slotted arm AC as shown in Figure Q3. The disk rotates about a fixed axis through point o at an angular velocity of w = 15 rad/s in counterclockwise direction causing the piston D to move in the vertical slot. The lengths of AB, BC and CD are 30 cm each and the radius of the disk, r= 15 cm. Determine at the instant when = 45°, B = 15°, and B is directly above O, i) the angular velocity of slotted arm AC, the velocity of point C, and iii) the velocity of piston D. [CO2/PO2/C4) (13 marks) c) Evaluate the angular velocity of slotted arm AC in Figure Q3 if the disk has higher angular velocity. Justify your answer by using appropriate formulation. [CO3/PO3/C6] (2 marks) B D Figure Q3 B x 2 e A w

Answer 1

Page 1 (a) Vc a 6 plane motion as Uixed plane No slipping same as that of the Rolling motion mepresents the general it can be considered en higid Ubody combination of Amansational motion parallel to a 4. pure plus a pure notational motion about anlaxis berpendicular to the plane and going through the centre of mass. at the contact A = VA = 0, ie, e ground VA = 0 = Vc t w Xrale = 0 Vc f t W (-k) x re- wr = 0 = (Vc - wr) i = 0 | Vc = wr So, when there is no slip at the contact et an extra constrailt relates the transitional velocity and the angula velocity لا = A => vc с LL we equation which

Ver 2 Page ez <JK Page No 30cm WED R B5150 Б) — әре VD Se لم 3oam 15cm! 447 А at & 15 3oem WAC = No t w x r Blo VB = wr= -15X0.15 i wo =-2.25 i miei cib VB w (k) x r Let B' be the point on the slotted lever, and geometrically coincident with the point Bº VÁ + WAL XrB/A WACK x Irgal - cosoi tsino = WALIMBAL (- coso; - sinof) 0.212 WAC (-Î-Î za VBI = We have, ㅈ = Vboe VB .ee WALIM BIAI (- cosoſ - sino?). (-sinoi-coso -wrcês.t-singi-cosoj)

Page 3 Date => WAHABAT from otsine) = wr sind rico wr sino IMBA) = 15x0.15 x sin 45 0.3 (*) -5.303 Madis To - (ம்) WAL X MCA + VÁ 5.303 Ř x 0.6(-cosoit sino) Vc -2.257 -2.25 ملا متن Vc + WCD X role Voj Vo = ve t wro ħ x 0.3 (cosis î+ sinis) = Ve + 0.3 Wcb fcosisi-sinisi) voj - 2.259 – 2.23î +0.29 wcoj -0.078w.com 2.25 - 0.078 WED 0 =) wo = -28.85 wao = 28.85 (R) the clockwise) ?

Page 4 Tage No. A VE - 2.25 +0.29 WED => -10.62 to.62 (t mys VD cey From (*) we have r WAE sin o ALBA Now we have, sino<1 r <1 "B/A) =) WAC (w