Question

Problem 3. (2 points, adding to your overall grade, up to 4.0) A small 4-lb collar C can slide freely on a thin ring of weight 6 lb and radius 10 in. The ring is welded to a short vertical shaft, which can rotate freely in a fixed bearing. Initially the ring has an angular velocity of 35 rad/s and the collar is at the top of the ring (0 = 0) when it is given a slight nudge. Neglecting the effect of friction, determine a) the angular velocity of the ring as a function of e. (1 point) b) the velocity of the collar relative to the ring as a function of O. (1 point)

A small 4-lb collar C can slide freely on a thin ring of weight 6 lb and radius 10 in. The ring is welded to a short vertical shaft, which can rotate freely in a fixed bearing. Initially the ring has an angular velocity of 35 rad/s and the collar is at the top of the ring (θ = 0) when it is given a slight nudge. Neglecting the effect of friction, determine a) the angular velocity of the ring as a function of θ. (1 point) b) the velocity of the collar relative to the ring as a function of θ. (1 point)

Answer 1

2 T. 2 (v.), "R R С x n 2 (Mat 2n) R² (mptome) R22 - MR heat / me voy The law of Conseovation of energy gives the Let us draw the free body diagrams of the systery at initial position, wi= 35 radis we get FR = 2 MP R @ Draw the FBD at final Position .. (vely = Roy ,1 Iph, = I want me vey 12 pr. wol = Mercy 2 wer wat mewah 2 met Rhoz + WR2 (MR + zme R²02 t me true 6/32:2 6/32.2 + 2.4/322 b) we know KiE = Dw Т) Ź IRLO Law & R²) 20, 2 a potential energy = PE PE = v=mcor ...At final positroy KE = T2 = I T2 = /4 MR RW ² T 2 - 1/2 MAR? ме е?», wi WR R2 2 7 ws 35 W2 = 15 rad w2= S 6 2 2 2 2 CX 2 Ta tuz ocy T + V timp.R?o? the gr = (t amet me ) RW Et me -> 4x6x10735+4832:2x10 FLEST) 315"tź.4. very 39.6286 t 3.333 16-983 + 0.062(V); 20.5 ftls Very