physics
posted by valem .
A 15.5m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.42 kg · m2, and its radius is 0.170 m. When the reel is turning, friction at the axle exerts a torque of magnitude 3.63 N · m on the reel. If the hose is pulled so that the tension in it remains a constant 23.1 N, how long does it take to completely unwind the hose from the reel? Neglect the mass of the hose, and assume that the hose unwinds without slipping.

The applied torque minus the frictional torque is (23.1)(0.170)3.63 = 0.28 Nm
Torque divided by moment of inertia is the angular acceleration, alpha. Its units are radians/s^2. Calculate it
To unreel all of the hose, you need to turn the reel through 15.5/0.17 = 91.1 radians.
Solve this equation for the required time, t:
91.1 radians = (1/2)*(alpha)*t^2