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Tutorial Exercise A 107-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.950 rev/s in 2.00 s? Step 1 The diagram below shows the view of the merry-go-round from above. The moment of inertia of a uniform, solid disk of mass M = 107 kg and radius r = 1.50 m is 1 = 1Mr2 107 107 kg) 1.50 | 1.5 m) = 120.36 120 kg . m. Step 2 The desired angular acceleration a for the merry-go-round, where w is the final angular speed, Wo the initial angular speed, and At the time interval from rest, is given by w - wo At rev/s) - 0 rev/s ? ) ( 2It radrad/3 2.A grinding wheel is in the form of a uniform solid disk of radius 6.96 cm and mass 1.99 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.593 N . m that the motor exerts on the wheel. (a) How long does the wheel take to reach its final operating speed of 1 210 rev/min? 14.8 1X If you know the change in velocity and the acceleration you can certainly find the time. Can you determine the (angular) acceleration? s (b) Through how many revolutions does it turn while accelerating? 21 1x You know the initial and final (angular) speeds and the time. Can you use constant acceleration equations to determine the (angular) distance traveled during this time interval? rev Need Help? Read It