Question

B1. As shown in Figure Bl, a horizontally-directed force P is applied to a homogenous disk weighted W with radius ofr. P y G Figure B1 (a) Draw the free body diagram of the disk. (4 marks) (b) Show the moment of inertia Ig about point G of the disk as follow: (where mis mass of the disk): mur? (4 marks) 2 (c) Considering force equilibrium in x- and y-directions and also the moment equilibrium about point G, derive the expressions of i) angular acceleration a, ii) friction F, and iii) normal force N between the plane and disk. Assume that the disk rolls without sliding on the ground. (8 marks) (Take acceleration of gravity as g) (d) If the same disk is modified with a hollow, explain how would the resultant angular acceleration be affected? (4 marks)

Answer 1

moment of interfa of small section about a FBD of disk Fy Ace") L Р x (Angular de →a (Ach of c.m) VW Norbert F ( friction fosie) N Rolls without shidding. (28=a) by moment of intentad about a dre memass of disk 22 radius of disk С. take small seetmlare) M mass of smass section dm) = -Y(202&due) re2 dm - m. x(2rUdx) T2² am 2m. redu &2

dela) = dm.222 -> d (IM) = 2m. (udre) . 2² = 2m 203 dre: 82 &2 For full disk r (d(In) = zly (2²dx) 82 & -> In = 2 m 쭩 LI 2m (at) 22 4 Iq = me2 2 Proved 2 a from FB D Nam mg Answer cilis Efy=0 W-N =0 ) Ern=toma ) P-f=ma -O Ema lux -> PY+ Fra - Ia a = PY+FR = In ( a ) [a=&&] 2 - PY + F = Ia h from qqn & (2) P(++) im+ (1/8 EEEEEEEEEEEE

. me2 [ur 2, Answer disc is modified with <ix Angulus Aceh P(1+x) 2.m + m2 x = 2P (kty) 3m 22 Friction force. p-ma = P2P (2+ Y)<xm 3m 82 P 2PY 3. 38 Answer hollow if same moment of intertia is change fa=m&2 KUTY a d) Li- P(1+x) rmt 1tm4² 22 da P (2+Y) 2 m2 m Answer

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