A). A drum rotatesat an angular velocity of 12.6rad/s . If the drum starts slowi

Question

A). A drum rotatesat an angular velocity of 12.6rad/s. If the drum starts slowing down at a rate of4.2 rad/s2. i). How much time does it take tocome to rest? ii). Through what angle does itrotate in coming to rest? --------------------------------------------------------------------------------------------------------- B). The figureshows a uniform disc with mass M = 2.5 kgand radius R = 20cm, mounted on a fixed horizontal axle. A block withmass m =1.2 kghangs from a massless cord that is wrapped around the rim of thedisk.
Find the acceleration of the falling block, the angularacceleration of the disk and the tension of the cord Assume : the cord does not slip andthere is no friction at the axel --------------------------------------------------------------------------------------------------------- i). How much time does it take tocome to rest? ii). Through what angle does itrotate in coming to rest? --------------------------------------------------------------------------------------------------------- B). The figureshows a uniform disc with mass M = 2.5 kgand radius R = 20cm, mounted on a fixed horizontal axle. A block withmass m =1.2 kghangs from a massless cord that is wrapped around the rim of thedisk.
Find the acceleration of the falling block, the angularacceleration of the disk and the tension of the cord Assume : the cord does not slip andthere is no friction at the axel --------------------------------------------------------------------------------------------------------- Assume : the cord does not slip andthere is no friction at the axel --------------------------------------------------------------------------------------------------------- Assume : the cord does not slip andthere is no friction at the axel ---------------------------------------------------------------------------------------------------------

Explanation / Answer

A) i) we know that                            = o + t            ==>o = - t            ==>t = - o / = - 12.6 / -4.2 = 3.0 s    ii) = * t - 0.5 t2   = - 0.5 t2 = - 0.5 * -4.2 * 3*3 = 18.9 deg B) = a / R     Where a = -2mg / (M+2m) = - 2 * 1.2 * 9.8 / (2.5+ 2.4) = -4.8 m/s2    ==> = -4.8 / 0.2 = - 24 rad/s2

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