A reel of flexible power cable is mounted on the dolly, which is fixed in position. There are 190 ft of cable weighing 0.402 lb per foot of length wound on the reel at a radius of 14 in. The empty spool weighs 65 lb and has a radius of gyration about its axis of 11 in. A tension T of 15 lb is required to overcome frictional resistance to turning. Calculate the angular acceleration α of the reel if a tension of 33 lb is applied to the free end of the cable.

Explanation:

Total mass of cable m = 190 x .402 = 76.38 lb

moment of inertial due to this cable = m r²

= 76.38 x (14/12)²

= 103.96 lb ft²

moment of inertia of empty spoon

= mR² where R is radius of gyration

= 65 x (11 / 12 )²

= 54.61 lb ft²

Total moment of inertia I = 158.57 lb ft²

Net force applied = force applied - frictional force

= 33 - 15 = 18 lb

= 18 x 32 poundal

= 576 poundal

Torque applied = force x radius

= 576 x 14/12

= 672 unit

Angular acceleration = torque / total moment of inertia

= 672 / 158.57

= 4.238 radian / s²

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