Question

The disk of radius r = 1.5 m rolls without slipping on the incline with angle 0 = 30°. Simultaneously, the small particle A moves along the slot located at distance d = 0.3 m from the center of the disk. At the instant shown, the disk has a constant clockwise angular speedw = 1 rad/s, and the particle is in position x = 0.4 m which is increasing at a constant rate į = 1.3 m/s. Determine the magnitude of the total acceleration of the particle A at the instant shown. Give your answer in m/s2. (

Answer 1

Giren &=1.5m d-0.3m x=0.am V = x= 1.3m/8 (Constant) Woo rad's O=30° It is given that instantaneous centre of rotation is B as the disc rolls without slikking. lanl= worx AB 0.3 O 3686 302 = 15m 30° A R=ſd²tr2 = 0.5m B o= tant (4) = 53.13° using some rule R Sn (180-66.86-0) 11 smo AB Sm 66.86° 0.5 1.5 Sin (113-14-0) Sno Sin 66.86° Sind = 3 áin (113-11-D » 0 - 93.79

- AB - 1.5 Sin 8370 * sin(66.860) = 1.38 22 m 1.3822 so m/s2 lanl= wa XAB (092x ( 3822)
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