Any help would be appreciated. I have tried multiple times and come up with an i

Question

Any help would be appreciated. I have tried multiple times and come up with an incorrect answer.

A 50 kg winding drum 75 cm in diameter is used to reel in cable. It is moving at the rate of 2 revolutions per second. The rotation rate then increases by 5.25 rad/s^2 for the next 1.5 seconds. It rotates at the new rate for three seconds. Finally it comes to a stop in one and one half rotations. What was the total length of cable coiled around the drum during the entire time? Answer: 35.8 m Here's a hint on how I attempted to solve it but didn't come up with the correct answer. Three parts acceleration for 1.5 seconds Constant velocity for 3 seconds Stopping in 1.5 revolutions Calculate the angle Theta for each part and sum.

Explanation / Answer

radius of the drum, r = d/2

= 75/2

= 37.5 cm

= 0.375 m

initial angular velocity, w1 = 2 rev/sec

= 2*2*pi rad/s

= 12.56 rad/s

from the given data, angular acceleration, alfa1 = 5.25 rad/s^2

angular displacement in first 1.5 s, theta1 = w1*t + 0.5*alfa*t^2

= 12.56*1.5 + 0.5*5.25*1.5^2

= 24.75 rad

angular velocity after 1.5s, w2 = w1 + alfa*t

= 12.56 + 5.25*1.5

= 20.44 rad/s

angular dispalcement in next 3 s, theta2 = w2*2

= 20.44*3

= 61.32 rad

angular dispalcement in the last case, theta3 = 1.5 revolsuions

= 1.5*2*pi

= 9.425 rad

total angular displacement, theta = theta1 + theta2 + theta3

= 24.75 + 61.32 + 9.425

= 95.495 rad

now Apply, s = r*theta

= 0.375*95.495

= 35.81 m <<<<<<<---------Answer

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