Question

<Homework for MO3.2 14 of 17 Rotation about a Fixed Axis A Review Part B Learning Goal: To use the kinematic relationships for rotation about a fixed ads to determine the number of revolutions for an accelerating pulley The two pulleys shown in (Figure 1) are connected by a belt, which is assumed to not slip with radila = 30 mm and re - 60 mm. Pulley A has been spinning at a constant WA = 4 rad/s Att0 pulley A is accelerated at a(t) = 18e How many revolutions does pulley B go through from t = 0 tot 4s? Write a function to describe the angular acceleration of pulley B fort 0 Express your answer in terms of t so that ag is in rad/swhen t is in seconds. View Available Hint(s) ΟΙ ΑΣφ HT ? vec ayo rad/ Submit - Part C Write a function to describe the angular velocity of pulley B. Express your answer in terms of t so that wg is in rnd/s when t is in seconds ► View Available Hints) ΤΟΙ ΑΣφ Figure < 1 of 1 > vec ? B rad/s Submit Type here to search o E E 8

Answer 1

Given that i- B I A = 30mm {o=Gomm WB = ?? WA = 4 rad/s, ,to da 18 e 3t &B = ?? Can see from data that radius pulley A is giren radius of pulley half the which means B old 2 2K rA 20 rb Circumference A Circunference of pulley - of Pulley 2 of fulley A & means lie, Crocumference half the Circumfuence which single rotation pulley B will be notated by haly of bulley 3 giving pulley A

Pulley A requires a godation for squead single Jotation of pulley B. depicts 2 NA 2. NB (whe where i dopunta ) rotation -NA (2ANB) x2 WA -2.WB lie, pulley A will have twice the angular velocity of pulley Differentiating equation (with respect to time deos na dwa A 2. at dt 2do LA Lo 2 be the lie Angular acceleration angular acceleration J B will half of of A Is e 3t La 2 9 e 3t (Answer, part 3)

know that x dew at where angular acceluation angular relocity t time Sa.de sa y WB = at B s gest de r3t ge -3 + c WB c -3 e 3t to Given that CA = 4oad/s* at at too means 2 Ws t-o u 2 WB t-o WBT 2 and/s at to purting this condition in equation @ 2 = -3x0 - 3e tc 2 = - 3tc c=5

ap we 12 5 - 363 ( Answer og part c) for No. ratations from J secs to to tozu & 3 B = [cogItz [cgIt [s-3eory] - [s- geson 2.99998 sad/s2 جد) ༈ ། as WB 2x No 2.99998 Go NB 28,647 revolutions

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